The bisectors of angle A and C of a quadrilateral ABCD intersect each other at P. Then P is equidistant from the opposite sides AB and CD.

True

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False

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Solution

The correct option is A
True

We know that the locus of a point which is equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines and that any point on the bisector of the angle formed by two intersecting lines is equidistant from those two lines.

Since P lies on the bisector of angle B, P is equidistant from AB and BC ------ (1)

Since P lies on the bisector of angle C, P is equidistant from BC and CD ------ (2)

From (1) and (2), P is equidistant from AB and CD.

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