Question

Abc is a right triangle in which angle b =90. If ab=8cm bc=6cm.Find the diameter if thd curcke inscribed inside

Answer 1

Answer:

4

Step-by-step explanation:

By Pythagoras' Theorem, the hypotenuse ac has length:

ac = √( ab² + bc² ) = √( 64 + 36 ) = √100 = 10

The semiperimeter of the triangle is

s = ( ab + bc + ca ) / 2 = ( 8 + 6 + 10 ) / 2 = 24 / 2 = 12

The area of the triangle is

Δ = (1/2) base × height = (1/2) ab × bc = (1/2) × 8 × 6 = 24

The inradius is

r = Δ / s = 24 / 12 = 2

The diameter of the inscribed circle is twice the radius:

diameter = 2r = 4