In a triangle ABC , if AB = AC and AB is produced to D such that BD = BC , find ∠ ACD : ∠ ADC.

Question

In a triangle ABC , if AB = AC and AB is produced to D such that BD = BC , find &#x2220; ACD : &#x2220; ADC.

Philoid · Accepted Answer

Given,

AB = AC and,

BD = BC

∠2 = ∠3 (Since, AB = AC)

∠4 = ∠5 (Since, BD = BC)

= (i)

In

∠2 = ∠4 + ∠5

∠2 = 2∠4 (Since, ∠4 = ∠5)

∠3 = 2∠4 (Since, ∠3 = ∠2)

=

Thus, ∠ACD: ∠ADC = 3: 1

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.