Question

A circle with centre '0' touches all the four sides ofa quadrilateral. ABCD internally in such a way that it divides AB in 3:1 and AB = 12cm then find the radius of circle where OA = 15 cm.

Answer 1

Answer:

The radius of the circle = 12 cm

Answer 2

AP : BP = 3:1

AP = 3x, BP = x

AP + BP = AB

3x + x = 8cm

4x = 8

x = 8/4

x = 2cm

AP = 3*2 = 6cm

BP = 2cm

By Pythagoras theorem.

(OP) square = (OA) square + (AP) square

= (10)^2 + (6)^2

= 100 - 36

OP. = √64

OP. = 8 cm

Hence, radius of circle = 8cm