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Question

D is a point on side BC of ABC such that AD=AC.Show that AB>AD
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Solution

Given:AD=AC
Angles opposite to equal sides are equal
So, ACD=ADC .......(1)
Now, ADC is an exterior angle of ABD
ADC=ABD+BAD since exterior angle is sum of interior opposite angles.
So, ADC>ABD
ACD>ABD since side opposite to the greater angle is longer
AB>AD as AC=AD given
Hence proved.

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