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Question

In ΔABC, AC > AB and AD bisects A. Which of the following option is correct?


A

ADC ADB

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B

ADC ADB

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C

ADC = ADB

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D

None of these

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Solution

The correct option is A

ADC ADB


In ΔABC, it is given that AC > AB, which means B > C.

Now, AD bisects A,
So, in ΔADC, ADC = 180 - (A2 + C)
Similarly, in ΔADB, ADB = 180(A2 + B)

and since B in ΔADB is greater than C in ΔADC, and A2 is common (AD is the bisector),
we can deduce that ADB is smaller than ADC.


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