Question

Respected Sir,

Please help me in solving my below mentioned doubt:

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

Answer 1

In triangle BDC, BD = BC
so <BDC = <BCD

or <ADC = <BCD -------(1)

In triangle ABC, AB = AC
so <ABC = <ACB ------(2)

also, < A + <ABC + < ACB = 180 -----(3)

In triangle ADC,
<A + <ADC + <ACD = 180 -------(4)

from (3) and (4)
< A + <ABC + < ACB = <A + <ADC + <ACD
or <ABC + < ACB = <ADC + <ACD
or 2 <ACB = <ADC + <ACD (from (2)
or 2 (<ACD - <BCD) = <ADC + <ACD
or 2 (<ACD - <ADC) = <ADC + <ACD (from (1)
or 2 <ACD - 2<ADC = <ADC + <ACD
or 2 <ACD - <ACD = <ADC + 2<ADC
or <ACD = 3 <ADC
<ACD:<ADC=3:1