Question

In a triangle ABC , the angle A is externally bisected by a line which meets the base produced at D and circum circle at E,then prove that AB.AC =AE.AD .

Answer 1

Answer:

Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.

Prove that : BD / CD = AB / AC

Construction : Draw CE || DA meeting AB in E.

Statements

Reasons

1) CE || DA 1) By construction

2) ∠1 = ∠3 2) Alternate interior angle

3) ∠2 = ∠4 3) Corresponding angle (CE ||DA and BK is a transversal

4) AD is a bisector of ∠A 4) Given

5) ∠1 = ∠2 5) Definition of angle bisector

6) ∠3 = ∠4 6) Transitivity (from 2 and 4)

7) AE = AC 7) If angles are equal then side opposite to them are also equal

Step-by-step explanation:

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