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Answers posted by sreemathi.v
Questions
8823
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Two circles with centre A and B and of radii 5 cm and 3 cm touch each other internally.If the perpendicular bisector of segment AB meets the bigger circle in P and Q,then the length of PQ is ___________
answered
Jan 5, 2015
Answer : $4\sqrt 6$ cm
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In the given figure TAS is a tangent to the circle,with centre O,at the point A.If $\angle OBA=32^{\large\circ}$,then the values of $x$ and $y$ are _____
answered
Jan 5, 2015
Answer : $x=y=58^{\large\circ}$
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In the given figure chords AB and CD of a circle intersect at O.AO=5 cm,BO=3 cm and CO=2.5 cm.Then the length of DO=______
answered
Jan 5, 2015
Answer : 6 cm
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Two triangles ABC and DEF are similar to each other in which AB = 10 cm and DE=8 cm.The ratio of the areas of $\Delta ABC$ and $\Delta DEF$ is _____
answered
Jan 5, 2015
$ \frac {ar (\Delta ABC)}{ar (\Delta DEF)} = \frac {AB^2}{DE^2} = \frac {BC^2} {EF^2} = \frac {AC^2}...
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If E is a point on side CA of an equilateral $\Delta ABC$ such that $ BE \perp AC$, then $ AB^2 + BC^2 + CA^2 = K BE^2 $. Then the value of K is
answered
Jan 5, 2015
https://clay6.com/mpaimg/55894.jpg$ BE \perp AC$$ AE = EC = \frac {a}{2}$$ In \Delta ABC, AB^2 = BE^...
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ABCD is a rectangle in which BC=2AB.A point E lies on ray CD such that CE = 2BC.Then BE _____ AC.
answered
Jan 5, 2015
Answer : perpendicular
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ABCD is a parallelogram.AB is divided at P and CD at Q so that AP : PB = 3 : 2 and CQ : QD= 4 : 1.If PQ meets AC at R,then AR =____ AC.
answered
Jan 5, 2015
Answer : $\large\frac{3}{7}$
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In a $\Delta ABC$,AD is a median .X is a point on AD such that AX : XD = 2 : 3.Ray BX intersects AC in Y.Then BX=______ XY.
answered
Jan 5, 2015
Answer : 4BX=4 XY.
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A point D is on the side BC of an equilateral triangle ABC such that $DC=\large\frac{1}{4}$$BC$.Then $AD^2$=____$CD^2$
answered
Jan 5, 2015
Answer : 13$AD^2=13 CD^2$
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ABC is a right angled triangle at A.BL and CM are its two medians,then $4(BL^2+CM^2)=$_______
answered
Jan 5, 2015
Answer : $5BC^2$$4(BL^2+CM^2)=5BC^2$
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If one diagonal of a trapezium divides the other diagonal in the ratio 1 : 2,then one of the parallel sides is ______ the other.
answered
Jan 3, 2015
Answer : doubleIf one diagonal of a trapezium divides the other diagonal in the ratio 1 : 2,then one...
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The perpendicular AD on the base BC of a $\Delta ABC$ intersects BC at D such that DB=3CD.Then $2(AB^2-AC^2)=$______
answered
Jan 3, 2015
Answer : $BC^2$
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In $\Delta ABC$.the bisector of $\angle A$ intersects BC in D.If AB=18 cm,AC=15 cm and BC=22 cm then BD=_____
answered
Jan 3, 2015
https://clay6.com/mpaimg/ETG56T7UH.jpg By angle bisector theorem :ABAC=BDBC" role="presentation" sty...
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In $\Delta ABC$,P and Q are points on sides AB and AC respectively such that $PQ\parallel BC$.If AP=4 cm,PB=6 cm and PQ=3 cm,then BC is ____
answered
Jan 3, 2015
Answer : 7.5 cm
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$\Delta ABC$ and $\Delta DBC$ are on the same base BC.Then $\large\frac{ar\;\Delta ABC}{ar\;\Delta DBC}$=______
answered
Jan 3, 2015
Answer : $\large\frac{AX}{DX}$
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In a $\Delta ABC,\angle BCA=90^{\large\circ}$ and Q is the midpoint of BC.Then $AB^2+3AC^2=$______
answered
Jan 3, 2015
Answer : $4AQ^2$$AB^2+3AC^2=4AQ^2$
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ABCD is a rectangle in which BC=2AB.A point E lies on ray CD such that CE=2BC.Then BE is _____ AC.
answered
Jan 3, 2015
Answer : perpendicular to
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In $\Delta PQR$,M and N are points on sides PQ and PR respectively such that PM=15 cm and NR=8 cm .If PQ=25 cm and PQ=20 cm ,then MN is ______ QR.
answered
Jan 3, 2015
https://clay6.com/mpaimg/6YGDVU.jpgAccording to B. P. T$\frac{PM}{PQ} = \frac{PN}{PR}$ PN = 20 - 8 =...
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The corresponding sides of two similar triangles are in the ratio 1 : 3.If the area of the smaller triangle is $40\;cm^2$,then the area of the larger triangle is ________
answered
Jan 3, 2015
Answer : $360\;cm^2$
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The value of $x$ in the adjacent figure if $DE\parallel AB$ is ______
answered
Jan 3, 2015
Solution : https://clay6.com/mpaimg/1_ap45.jpgIf $DE || AB$ then by Basic proportionality theorem $...
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An aeroplane leaves an airport and flies due north at a speed of $1000$ km/hr.At the same time,another aeroplane leaves the same airport and flies due west at a speed of $1200$ km/hr.How far apart will be the two planes after $1\large\frac{1}{2}$ hours?
answered
Jan 3, 2015
Answer : 2343 km (approx)
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The vertices of a triangle ABC are A(a-1)an B$(2\sqrt a)$an C(a+1)an is ________ triangle.
answered
Jan 3, 2015
Answer : right angled triangle
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In a quadrilateral ABCD,$\angle B=90^{\large\circ}$ and $AD^2=AB^2+BC^2+CD^2$,then $\angle ACD=$______
answered
Jan 2, 2015
Answer : $90^{\large\circ}$
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A wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.How far from the base of the poles should the stake be driven so that the wire will be taut?
answered
Jan 2, 2015
Answer : $6\sqrt 7$ mhttps://clay6.com/mpaimg/Triangle-5.pngLet AB be the pole of height 18 m.AC is ...
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votes
In $\Delta PQR$,M and N are points on sides PQ and PR respectively such that PM=15 cm and NR=8 cm.If PQ=25 cm and PR=20 cm,then MR is ________ QR
answered
Jan 2, 2015
Answer : parallel toMR is parallel to QR.
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ABCD is a trapezium in which $AB\parallel DC$.$P$ and $Q$ are points on sides AD and BC such that $PQ\parallel AB$.If $PD=18,BQ=35$ and $QC=15$,then $AD$=______
answered
Jan 2, 2015
Answer : 60AD = 60
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votes
A staircase is as shown in the figure.Measurements of the steps are marked in the figure.Find the distance between AB.
answered
Jan 2, 2015
Answer : 10 unitsDistance between AB is 10 units.
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$\Delta ABC$ is an isosceles triangle in which $\angle C=90^{\large\circ}$.If $AC=6$ cm,then $AB=$_____
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap46.jpgABC is an isosceles triangle $\angle C=90^{\circ}$ $AC= ...
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votes
In an isosceles triangle ABC if AC=BC,and $AB^2=2AC^2$,then $\angle C$=___
answered
Jan 2, 2015
Answer : $90^{\large\circ}$
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votes
ABCD is a trapezium such that $BC\parallel AD$ and $AB=4$ cm.If the diagonals AC and BD intersect at O,such that $\large\frac{AO}{OC}=\frac{DO}{OB}=\frac{1}{2}$,then $BC$=
answered
Jan 2, 2015
https://clay6.com/mpaimg/RFV33.jpgConsider $ \triangle AOB and \triangle COD$ $\angle AOB = \angle C...
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votes
$\Delta ABC$ is a right triangle,right-angled at A and $AD\perp BC$.Then $\large\frac{BD}{DC}$=____
answered
Jan 2, 2015
Answer : $\big(\large\frac{AB}{AC}\big)$$\large\frac{BD}{DC}=\big(\large\frac{AB}{AC}\big)$
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votes
In a $\Delta ABC,AD$ is the bisector of $\angle BAC$.If $AB=6$ cm,$AC=5$ cm,and $BD=3$ cm,then $DC$=
answered
Jan 2, 2015
https://clay6.com/mpaimg/4c3dea3.jpg AB = 6cm, AC = 5cm , BD = 3cm$\therefore$ AD is the bisector of...
0
votes
A man goes $24$ m due west and then $7$ m due north.How far is he from the starting point?
answered
Jan 2, 2015
https://clay6.com/mpaimg/6_Untitled.jpgAccording to pythagorus theorem $7^2 + 24^2 = x^2$$49 + 576 =...
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votes
$\Delta ABC\sim \Delta DEF$.If $BC=3$ cm,$EF=4$ cm and ar$(\Delta ABC)=54\; cm^2$,then ar$(\Delta DEF)$=
answered
Jan 2, 2015
$\triangle ABC \sim \triangle DEF$When 2 triangles are similar,then, $\frac{Area of \triangle ABC}{A...
0
votes
$\Delta ABC \sim \Delta DEF$,ar $(\Delta ABC)=9 cm^2$,ar $(\Delta DEF)=16 cm^2$.If $BC=2.1$ cm, then the measure of EF is
answered
Jan 2, 2015
$\triangle ABC \sim \triangle DEF$$\frac{Area of \triangle ABC}{Area of \triangle DEF} = \frac{AB^2}...
0
votes
$\Delta ABC \sim \Delta DEF$ such that $DE=3$ cm,$EF=2$ cm,$DF=2.5$ cm,$BC=4$ cm,the perimeter of the $\Delta ABC$ is
answered
Jan 2, 2015
https://clay6.com/mpaimg/54CGF.jpg $\triangle ABC \sim \triangle DEF$The corresponding sides are $\f...
0
votes
In a $\Delta ABC$ which is an equilateral triangle such that $AD\perp BC$,then $AD^2$=_____
answered
Jan 2, 2015
https://clay6.com/mpaimg/5TRVFDD.jpg $AC^2= AD^2 + DC^2$$AD^2 = AC^2 - DC^2$But BC = BD + DC AC = BD...
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votes
In an equilateral triangle ABC,if $AD\perp BC$,then
answered
Jan 2, 2015
Solution : $\Delta ABC $ is equilateral https://clay6.com/mpaimg/ap43.jpggiven $AB =BC = AC$,$AD \pe...
0
votes
ABCD is a trapezium such that $BC\parallel AD$ and $AB=4$ cm.If the diagonals AC and BD intersect at O such that $\large\frac{AO}{OC}=\frac{DO}{OB}=\frac{1}{2}$,then $BC$=
answered
Jan 2, 2015
Answer : $8$ cm
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votes
If D,E,F are the mid-points of sides BC,CA and AB respectivelyof $\Delta ABC$,then the ratio of the areas of triangles DEF and ABC is
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap44.jpgWe know that, the line joining the mid points of two sid...
0
votes
A vertical stick $12$ cm long casts a shadow $8$ cm long on the ground.At the same time a tower casts a shadow 40 m long on the ground.The height of the tower is _______
answered
Jan 2, 2015
Answer : $60$ m
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A ladder reaches a window which is 12 m above the ground on one side of the sheet,keeping its foot at the same point,the ladder is turned to the other side of the sheet to reach a window $9$ m high.The length of the ladder is $15$ m,then the width of the sheet is ______
answered
Jan 2, 2015
https://clay6.com/mpaimg/FC4D.jpg In $\triangle ABC$$\begin{align*}AB^2 + BC^2 & = AC^2 \\ 12...
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votes
The perimeters of two similar triangles are $30$ cm and $20$ cm respectively.If one side of the first triangle is $15$ cm,the corresponding side of the second triangle is _____
answered
Jan 2, 2015
https://clay6.com/mpaimg/g56cgvt.jpg
0
votes
In the given figure $AB\parallel MN$.If $PA=x-2,PM=x,PB=x-1$ and $PN=x+2$,find the value of $x$.
answered
Jan 2, 2015
Solution : $PA= x-2$$PB= x-1$$PM= x$$PN= x+2$By B.P.T theorem $\large\frac{PA}{PM} =\frac{PB}{PN}$=&...
0
votes
In the given figure,AD is the bisector of $\angle BAC$.If $BD=2$ cm,$DC=3$ cm and $AB=5$ cm,then $AC$=______
answered
Jan 2, 2015
Solution : given $BD= 2\;cm$$DC= 3\;cm$$AB= 5\;cm$$\large\frac{AB}{AC} =\frac{BD}{DC}$$\large\frac{5...
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votes
Two poles of height $7$ m and $12$ m stand on a plane ground.If the distance between their feet is $12$ m,then the distance between their tips is __________
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap42.jpg$AC^2=AB^2+BC^2$=> $AC^2=5^2+12^2$=> $AC= \sqrt {1...
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votes
The area of a right angled triangle if its radius is $3$ cm and altitude drawn to the hypotenuse is $2$ cm is ______
answered
Jan 2, 2015
Solution : If a right triangle is drawn inscribed in a circle then the mid point of hypotenuses will...
0
votes
In two similar triangles $ABC$ and $DEF,AC=10\;cm$ and $DF=8\; cm$ and $AB=6.5$ cm then $DE$=______
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap41.jpg$\large\frac{AB}{DE} =\frac{AC}{DF}$=> $\large\frac{6...
0
votes
In $\Delta$ ABC,DE$\parallel$BC.If $AD=x,DB=x-2,AE=x+2$ and $EC=x-1$,then the value of $x$ is _____
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap40.jpg$\large\frac{AD}{DB} =\frac{AE}{EC}$$\large\frac{x}{x-2}...
0
votes
The length of a diagonal of a rectangle whose adjacent sides are $8$ m and $6$ m long is _______
answered
Jan 2, 2015
Solution : https://clay6.com/mpaimg/ap39.jpg$AC^2 =AB^2 +BC^2$$\qquad= 8^2+6^2$$AC^2=100$$AC =10\;cm...
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