Question

two concentric circles have a common centre o. The chord ab of the bigger circle touches the smaller circle at p. if op=3cm and ab=8cm, then find the radius of the bigger circle

Answer 1

Answer:

Two concentric circles have a common centre O . The chord AB to the larger circle touches the smaller circle at P . If OP=3 cm and AB=8 cm, how would one find the radius of the larger circle?

Since chord AB is tangent to smaller circle at P , then radius OP is perpendicular to line segment AB at point P .

Let r= radius of larger circle.

Since points A and B are on larger circle, then OA=OB=r .

Since △OAB is isosceles (OA=OB) , then perpendicular bisector OP bisects AB .

AB=8 cm ⟹AP=BP=4 cm

Using Pythagorean theorem, we get:

r2=32+42

r2=25

r=5

Answer 2

Here is the solution..

Thankyou