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
Answers
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