Question

1. 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 ZCAB? Why?
(2) What is the distance of point C from
(3) d(A,B)= 6 cm, find d(B,C).
Practice set 3.1
a C 6 , a
line AB? Why?
(4) What is the measure of ZABC ? Why?
AB
Fig. 3.19
M​

Answer 1

Step-by-step explanation:

A.

∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

Thus, the measure of ∠CAB is 90º.

(2) Distance of point C from AB = 6 cm (Radius of the circle)

(3) ∆ABC is a right triangle.

CA = 6 cm and AB = 6 cm

Using Pythagoras theorem, we have

BC2=AB2+CA2⇒BC=62+62−−−−−−√ ⇒BC=62–√ cm

Thus, d(B, C) = 62–√ cm

(4) In right ∆ABC, AB = CA = 6 cm

∴ ∠ACB = ∠ABC (Equal sides have equal angles opposite to them)

Also, ∠ACB + ∠ABC = 90º (Using angle sum property of triangle)

∴ 2∠ABC = 90º

⇒ ∠ABC = 90°2 = 45º

Thus, the measure of ∠ABC is 45º