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Q)

# The circumradius of the $\Delta$le whose sides are $13,12\; and\; 5 \;is$?

$(a)\;15\qquad(b)\;\large\frac{13}{2}$$\qquad(c)\;\large\frac{15}{2}\qquad$$(d)\;6$

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A)
Toolbox:
• In any $\Delta\:ABC$, $\large\frac{a}{sinA}$$=2R$ where $R$ is circum radius and $a$ is side opp. to angle $A$.
Let the sides of the $\Delta$le be $a=13,b=12,c=5$
Now $a^2=b^2+c^2$
$(13)^2=(12)^2+(5)^2$
Hence the Pythogrous theorem is true.
$\Rightarrow \angle A=90^{\large\circ}$
We know that $R=\large\frac{a}{2\sin A}$
$R=\large\frac{13}{2\sin 90}$
$\;\;\;=\large\frac{13}{2}$
Hence (b) is the correct option.