Question

Isosceles Triangle ABC has each leg measuring 13 cm and is inscribed in circle O as shown below. If the altitude to the base of the triangle is 5cm, calculate the radius of the circle.

Answer 1

Radius = 5 + x

Also we have two similar triangles whose corresponding sides are proportional, hence:

Proportion may be 13 : 5 = (5 + x) : 13/2

5 · (5 + x) = 13²/2

5 x + 25 = 169/2

5 x = 169/2 - 25

x = 11.9

Then, R (radius) = 5 + x = 11.9 + 5 = 16.9 units