Question

If AP bisects $\angle$ BAC and M is any point on AP then the perpendiculars drawn from M to AB and AC are equal.
State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $△ABC$, AP bisects $\angle BAC$, $MQ\perp AB$,$MN\perp AC$
In $△AMQ$ and $△AMN$
$AM=AM$ (Common)
$\angle MAQ=\angle MAN$ (AP bisects $\angle A$)
$\angle MQA=\angle MNA$ (Each ${90}^{\circ }$)
thus, $△AQM\cong △ANM$ (ASA rule)
Hence, $MQ=MN$
Perpendicula and rs from M on AB and AC are equal