Question

In a triangle ABC, the bisector of the vertical angle A meets the base at D and the circumference
of the circum-circle at E. FEC is joined then
(A) AB.AD = AE .AC
(B) AB.AC = AE .AD
(C) AB .AE = AC. AD
(D) none of these​

Answer 1

The correct answer is (d) None of these.

What is the vertical angle bisector theorem?

• If a point is equidistant from the endpoints of a line segment in a triangle, it is on the perpendicular bisector of the line segment, according to this theorem. The perpendicular bisector, in other words, divides a given line segment into two equal portions to which it is perpendicular.

• Prove that if the bisector of a triangle's vertical angle bisects the triangle's base, the triangle is isosceles. Produce AD to E in such a way that AD = DE. ABC is isosceles, therefore join EC.

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