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Question
The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD.
Solution
Since P lies on the bisector of angle B,
Therefore, P is equidistant from AB and BC ...(1)
Similarly, P lies on the bisector of angle C,
Therefore, P is equidistant from BC and CD ...(2)
From (1) and (2),
Hence, P is equidistant from AB and CD.
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