Question

In $\Delta$ ABC, the bisector AX of $\angle$A intersects BC at X. XL $\perp$ AB and XM $\perp$ AC are drawn. Is XL = XM?

• A. No, they are in the ratio 1:2
• B. No, they are in the ratio 3:2
• C. Yes, they are equal
• D. No, they are in the ratio 2:3

Answer 1

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 $\angle$BAC. Therefore, X is equidistant from AB and AC.

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

Hence, XL = XM.