Question

Abc is a trangle in which angle b=90°, bc=48cm and ab=14cm. A circle is inscribed in the triangle, whose centre is o. Find radius r of in circle.

Answer 1

Answer:

Step-by-step explanation:

Given Triangle Δ ABC

Using Pythagoras theorem

BC² + AB² = AC²

48 ² + 14 ² = AC²

2304 + 196 = AC ²

2500 = AC²

√2500 = AC

500 = AC

Area of triangle ABC = 1/2 b ×h

                                      = 1/2 × 14 × 48

                                      = 336 cm ²

Semi perimeter o triangle by herons formulae

 S = a + b + c /2

S = 48 + 14 + 50 /2

S = 112 /2

S = 56 cm

Radius of circle = Area of triangle / Semi- perimeter of triangle

                        = 336 / 56

                        = 6 cm

Hence the radius of circle is 6 cm

Answer 2

use tangent property

you will get AC = 48-r +14-r =62-2r