Question

a circle is inscribed in a right triangle whose three sides are 6cm, 8cm and 10cm . find the radius of circle also find the area of portion which is not in circle ​

Answer 1

Answer:

The incenter of a triangle is equidistant from the three sides of the triangle, and the sides of the triangle are tangent to the inscribed circle.

The distance from a point to a line (or line segment) is the perpendicular distance. Therefor, at the right angle of the triangle, there is a square with a side length of r.

Tangent segments from the same point to the same circle are congruent.

Using the congruent tangents and the length of the hypotenuse we get:

⇒ (6−r)+(8−r)=10

solving for r

⇒ 14−2r=10

⇒ −2r=−4

⇒ r=2.

∴ The radius of the circle is 2 cm.