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Question

In ΔABC, AB is produced to D so that BD=BC. if B=60 and A=70, prove that: (i) AD>CD (ii) AD>AC

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Solution

Given : In ΔABC, side BC is produced to D such that BD=BC

A=70 and B=60

To prove :

(i) AD>CD (ii) AD>AC

Proof : In ΔABC,

A=70, B=60

But Ext, CBD+CBA=180

(Linear pair)

CBD+60=180

CBD=18060=120

But in ΔBCD,

BD = BC

D=BCD

But D+BCD=180120=60

D=BCD=602=30

and in ΔABC,

A+B+C=180

70+60+=180

130+C=180

C=180130=50

Now ACD=ACB+BCD

=50+30=80

(i) Now in ΔACB,

ACD=80 and A=70

Side AD>CD

(Greater angle has greatest side opposite to it)

(ii) ACD=80 and D=30

AD>AC


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