Question

A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.

Answer 1

The radius of circle is 5 cm

Explanation:

Given a right triangle △ABC with right angle C is inscribed in a circle in which

m∠C = 90°, AC = 8 cm, BC = 6 cm

we have to find the radius of circle.

As ACB is right angles triangle where angle C is right angle.

⇒ side AB must be the diameter of circle as angle made at semi circle is 90°

`Radius=AO=(1)/(2)AB`

By Pythagoras theorem

`AB^2=AC^2+CB^2`

`AB^2=8^2+6^2=64+36=100`

`AB=10cm`

`Radius=AO=(1)/(2)AB=(1)/(2)* 10=5cm`

Hence, the radius of circle is 5 cm