Question

In the adjoining figure the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.
(1) What is the measure of ∠CAB ? Why ?
(2) What is the distance of point C from line AB? Why ?
(3) d(A,B)= 6 cm, find d(B,C).
(4) What is the measure of ∠ABC ? Why ?

Answer 1

From the figure the radius of the

circle with centre C is 6cm .

Line AB is a tangent at A .

1 ) The measure of <CAB = 90°

By the theorem ,

The tangent at any point of a circle

is perpendicular to the radius through

the point of contact.

2 ) The distance of point C from

line AB = 6cm

Since , AB = radius = 6cm

3 ) d(A,B) = 6 cm , AB = 6 cm

d(B,C)= ?

Here ,

∆ABC , <CAB = 90°

BC² = AC² + AB²

[ By Phythogarian theorem ]

=> BC² = 6² + 6²

= 36 + 36

= 72

BC = √72

BC = √2×(6×6)

BC = 6√2 cm

d(B,C) = 6√2 cm

4 ) In ∆ABC ,

AB = AC = 6 cm

<ACB = <ABC

[ Since , Angles opposite to equal

sides are equal ]

<ABC + <ACB + <CAB = 180°

[ Angle sum property ]

=> <ABC + <ABC + 90° = 180°

=> 2<ABC = 180 - 90

=> <ABC = 90/2

=> <ABC = 45°

••••

Answer 2

HOPE IT HELPS YOU!!!