Given : $OT = 13 cm$$OP = 5 cm$$\Delta OPT, \;\;\; OP^2 + PT^2 = OT^2$$\implies 5^2 + PT^2 = 13^2$$...

Given$OP = 4\; cm$; $\angle{OPA} = 30^{\circ}$$\therefore AP = ?$$\frac{AP}{OP} = \cos 30^{\circ} = ...

$\Delta PAB ,\; PA = PB $ (equal tangents )$\therefore \angle{PAB} = \angle{PBA}$.$\implies \angle{A...

$PA \times PB = PC \times PD$$\therefore PA = PB + AB $$\qquad = 3 + 5$$\qquad = 8 \;cm$$\implies 8...

Solution :https://clay6.com/mpaimg/1_corr14.jpgArea of the shaded region = Area of the two semicircl...

Perimeter =$ 108$ cm$\implies \frac{1}{2} (2 \pi r) + 2r = 108$$\qquad \pi r + 2r = 108$$\implies \f...

https://clay6.com/mpaimg/ap33.jpgIn $\Delta OAB,AB=OA=OB(radii)$Hence $\Delta OAB$ is an equilateral...

Given :QP = 4.5 cmQP = PTAlso PT = PRPR = 4.5 cmQR = 4.5 + 4.5 = 9 cm

Since lengths of the tangents from an exterior point to a circle are equal.$\therefore \qquad AF ...

$\angle{ORD} = \angle{OSD} = 90^{\circ}$Also $OR = OS$$ORDS$ is a square $BP = BQ, \; CQ = CR, \; DR...

https://clay6.com/mpaimg/ap37.jpg$PQ = 8 \;cm$$OP =5 \; cm$$OL = 3\; cm$Let $TP =y $ and $TL=x$In $\...

Answer : $8\sqrt{2}\;cm$

$\Delta$AEO is similar to $\Delta$ABC$\angle{A} $ is common angle$\angle{AEO} = \angle{ABC} = 90^{\c...

$CP = CQ$ and $PA =AR$ and $QB = BR$Given $CP = 11 \; cm$ and $BR = 4\; cm$$\therefore CQ = 11 \;cm$...

Answer : 30 cmSince lengths of the tangents from an exterior point to a circle are equal,$\therefore...

Let the radius of the circle be $r$ and side of the square be $a$.Then, according to question $2 \pi...

Here Diameter of circle = Radius of semicircle = r" role="presentation" style="position: relative;"...

Let radius of the circle be $r$ cmThen according to question$2 \pi r - r = 37$$\implies r (2 \pi - ...

Solution :Let the radius of the circle be $r$ and the side of the square be $a$.Then according to th...

$D = 12''$$r = 6''$$\therefore Area = \pi r^2 = 36 \pi$$\frac{4.5 \pi}{36 \pi} \times 100 = 12.5 \%$...

$2 \pi R_2 - 2 \pi R_1$$10 \pi - 4 \pi = 6 \pi$$2 \pi (R_2 - R_1) = 6 \pi$$\implies R_2 - R_1 = 3$

$r = 18\; inches $$\begin{align*} Circumference & = 2 \pi r \\ & = 36 \pi \;inches \\ & ...

https://clay6.com/mpaimg/1345_a.jpg $OP^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2$$OP^2 = (8-3)^2 + (10-5)^2...

$\begin{align*} \text{Perimeter of the fence is }&= 2l + \omega + \pi r \\ & = 30 +7+ 11 \\...

Let the diameter be $x$.Then its area is $\pi (\frac{x}{2})^2 = \pi \frac{x^2}{4}$If it increases by...

One minute = $\frac{360^{\circ}}{60} = 6^{\circ}$$\therefore $ for $30^{\circ}$, the time is $\frac{...

$a^2 = 49$$a = 7\;in$Since the side of the square is the same as the diameter, then the radius is $\...

Let the area of the original circle be $\pi r^2$.If the new radius is $2r$, then the new area is $...

$\pi r^2 = 154$$\implies r^2 = 154 \times \frac{7}{22} = 7 \times 7$$\implies r = 7$$\begin{align*} ...

Let the radius of circle A be $x$, then the radius of circle B is $3x$.area of circle =πr^2=1^:3^2=1

The original radius = 5The new radius = 10Hence the new area will be $100 \pi$

$2 \pi r = 10 \pi$$\implies r = 5$Area = $\pi r^2 = 25 \pi$

Area of the shaded region = Area of the circle - Area of the triangle$\begin{align*}\text{Area of th...

Total area of both the circles is $4 \pi + 4 \pi = 8 \pi$Area of the overlapping region = $\pi$$\the...

$ 2 \pi r = 7 \pi$$\implies r = \frac{7}{2} = 3.5$$\therefore D = 2 \times r = 7$

Area of the circle = $22 \pi$$\implies \pi r^2 = 22 \pi$$\therefore r^2 = 22 $ or $r = 4.69$or diam...

$\begin{align*} \text{Area of the sector} & = \frac{30}{360} \times \pi r^2\\ & = 3 \pi \end...

Cost of summer upkeep = $ \$ 3.00\; per. sq. foot$Required area = area of the square + area of the ...

Solution :https://clay6.com/mpaimg/2_corr13.jpg$PQ=3RS$$OQ=20$$OR=10$$OP=?$$OPS \approx ORQ$=> $\...

$OD \perp AB$. The perpendicular drawn from the centre of the chord bisects the chord.Hence $AD = DB...

$C = 2 \pi r$$ \; \; = 2 \pi . \pi = 2 \pi^2$

Circumference of the circle = $2 \pi r$$\begin{align*} \text{Arc length} =& \frac{angle \; A}{2 ...

https://clay6.com/mpaimg/1174_a.jpgPerpendicular drawn from the centre to the chord bisect the chord...

By Pythagoras theorem: $OA^2 = OD^2 + AD^2$$\begin{align*} (ie) OA^2 & = 5^2 + 4^2 \\ & = ...

$a^2 = 400$$a = 20 \; \; \;\implies $ side of the square box is 20 inches.The diameter of the pizz...

Cake I : $\frac{360}{45} = 8\; pieces $Cake II : $\frac{360}{60} = 6 \; pieces$Revenue for Cake I i...

The complete angle in a clock is $360^{\circ}$.Each number represents an angle and the separation be...

The measure of angle formed by two secant to a circle from a point outside the circle is equal to ha...

https://clay6.com/mpaimg/1171_a.jpg When two chords intersect inside a circle, they cut in such a wa...

Given $m \angle A > m \angle B$ also $m \angle C=45^{\circ}$ $m \angle A $ is the greatest ang...