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.

Answer 1

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