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

Answer:

5

Step-by-step explanation:

Answer 2

Answer:

The radius is $r=5\ cm$

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

$m$

$m$

substitute

$90\°=(1/2)[arc\ AB]$

$arc\ AB=180\°$

That means----> The length side AB of the inscribed triangle is a diameter of the circle

Applying Pythagoras Theorem

Calculate the length side AB

$AB^{2}=AC^{2}+BC^{2}$

$AB^{2}=8^{2}+6^{2}$

$AB^{2}=100$

$AB=10\ cm$ -----> is the diameter

Find the radius

$r=10/2=5\ cm$ -----> the radius is half the diameter