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Question

In Δ ABC, the bisector AX of A intersects BC at X. XL AB and XM AC are drawn. Is XL = XM?


A

No, they are in the ratio 1:2

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B

No, they are in the ratio 3:2

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C

Yes, they are equal

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D

No, they are in the ratio 2:3

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Solution

The correct option is C

Yes, they are equal


We know that every point on the bisectors of the angle between two intersecting lines is equidistant from the intersecting lines.

Here, X lies on the bisector of BAC. Therefore, X is equidistant from AB and AC.

It is given that XL AB and XM AC. Therefore, the distance of X from AB and AC are XL and XM respectively.

Hence, XL = XM.


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