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Question
In figure , ABC is an isosceles triangle inscribed in a circle with centre O such that AB = AC = 13 cm and BC = 10 cm .Find the radius of the circle.
Solution
Since ABC is an isosceles triangle, AOO is the perpendicular bisector of BC.
In triangle ADC, by Pythagoras theorem we have
AD2 = AC2 - DC2 = 132 - 52 = 169 - 25 = 144
⇒ AD = 12 cm ⇒ AO + OD = 12 ⇒ AO = 12 - x ...(Assuming OD = x cm)
Again in triangle OBD,
BO2 = BD2 + OD2 = 25 + x2 ..(As BD = 5 cm)
⇒ (12 - x)2 = 25 + x2 ..(As AO = BO = radius)
⇒ 144 + x2 - 24 x = 25 + x2
⇒ -24 x = 25 - 144 = - 119
⇒ x = 4.96 cm
⇒ AO = 12 - 4. 96 = 7 .04 cm
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