12 In a triangle ABC, the bisector of the vertical angle A meets the base at D and the - Maths - Triangles

Question

12 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 If EC
is joined then
(A) AB AD = AE AC (B) AB AC = AE AD (C) AB AE = AC AD (D) none of
these

Brijendra Pal · Accepted Answer

Hi,

<img alt="" src=
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In triangle ACD and ABE angle ADC = angle BDE and angle ACB = angle AEB because AB is common chord and these two angles are in same side of chord So △ACD~△AEB AA similarityACAE= ADABAC×AB = AD×AE

12. 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. If EC is joined then (A) AB.AD = AE.AC (B) AB.AC = AE.AD (C) AB.AE = AC.AD (D) none of these

12. 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. If EC is joined then
(A) AB.AD = AE.AC (B) AB.AC = AE.AD (C) AB.AE = AC.AD (D) none of these