Question

The equal sides of an isosceles triangle are 8 cm long and the radius of its circumcircle is 5 cm. Calculate the length of its third side.

Answer 1

ΔABC is an isosceles triangle The bisector of ∠A bisects BC

OM = x; BM = \(\sqrt{5^2-x^2}\)

When we consider ΔAMB,

AB² = AM² + BM²

82 = (5 + r)² + \((\sqrt{5^2-x^2})^2\)

64 = 25 + 10x + x² + 25 – x²

64 = 10x + 50

14 = 10x

x = 14/10

= 1.4

BM = \((\sqrt{5^2-1.4^2})\)

BC = \(2(\sqrt{5^2-1.4^2}=2\sqrt{23.04}=\sqrt{92.16}\)

= 9.6 cm