Math, asked by saptakbhoumik, 4 months ago

In the given figure, ABC is a triangle and E is a point on side BC. If AE produced meets the circumcircle of AABC at D and CE = 2.5 cm, find the measure of line segment CD​

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Answers

Answered by vpraveena000
1

Step-by-step explanation:

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=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.

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