In a right-angled triangle ABC with right angle C, side AC is 6, BC is 8. Find the radius of the inscribed circle.

It is known:

Right-angled triangle ABC;
A circle is inscribed in the rectangle.
Angle C – straight;
Side AC = 6;
BC = 8.
Find the radius of the inscribed circle.

Solution:

Let’s write down the formula for the radius of the inscribed circle.

r = (AC + BC – AB) / 2;

AB hypotenuse is unknown. Let’s find it by the Pythagorean theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2;

AB = √ (AC ^ 2 + BC ^ 2);

AB = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.

Now let’s find the radius of the inscribed circle.

r = (AC + BC – AB) / 2 = (6 + 8 – 10) / 2 = (14 – 10) / 2 = 4/2 = 2;

Hence, r = 2.