A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 5 Marks · March 2023 · Standard

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1005 Marks · March 2023 · Standard
A triangle $ABC$ is drawn to circumscribe a circle of radius $4$ cm such that the segments $BD$ and $DC$ are of lengths $10$ cm and $8$ cm respectively. Find the lengths of the sides $AB$ and $AC$, if it is given that area $\triangle ABC = 90 \text{ cm}^2$.
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Join $OA, OB, OC$ and draw $OE \perp AC$ and $OF \perp AB$.
$BF = 10$ cm, $CE = 8$ cm, Let $AF = AE = x$
$ar \triangle ABC = ar \triangle BOC + ar \triangle COA + ar \triangle AOB$
$90 = \frac{1}{2} \cdot 4 (BC + CA + AB)$
$90 = 2(18 + 8 + x + 10 + x)$
$90 = 4(18 + x)$
$x = 4.5$
$AB = 14.5$ cm and $AC = 12.5$ cm
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