Question

3) In the fig. points B and C lie on tangent to the circle, touches at point A.
chord AD chord ED
If marc EF) = (are AD) and (arc DE) = 84
then determine :
i) mZDAC ii) mZFDA ii) mZBAF​

Answer 1

Step-by-step explanation:

Mathematics Part - II (Solutions)

CIRCLE

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 ∠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) It is given that line AB is tangent to the circle at 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=6

√

2

cm

Thus, d(B, C) = 6

√

2

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