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 = 18 cm, m∠B = 30°. Find r.

Answer 1

18 cm

Explanation:

find the hypotenuse using 30, 60, 90 rule then divide it by 2 to find the radius

P.S. posting all of the RSM questions aren't you

Answer 2

The radius is 18 cm

Explanation:

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

Also, AC = 18 cm, m∠B = 30°

we have to find the radius of this circle.

In ΔABC

`\sinB=(AC)/(AB)=(18)/(AB)`

`AB=(18)/(\sin 30)=(18)/((1)/(2))=36cm`

As given right angle i.e angle C is of 90° which is angle formed in the semicircle. Hence, the hypotenuse side must be the diameter of circle.

Diameter=36 cm

`Radius=(1)/(2)* diameter=(1)/(2)* 36=18 cm`