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