Question:
In ΔABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.
Solution:
Given: In ΔABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in X.
In $\Delta A B X$,
$\because \angle B A X>\angle A B X$
$\therefore B X>A X \quad \ldots(\mathrm{i})$
Similarly, in $\Delta A C X$,
$\because \angle A C X>\angle X A C$
$\therefore A X>C X \quad \ldots$ (ii)
From (i) and $(i i)$, we get
$B X>A X>C X$
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