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Question

P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects that angle between them
570019_5661545e258548adb5c461368223bfdd.png

Solution
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You are given that lines l and m intersect each other at A.

Let PB is perpendicular on l and

PCm. It is given that PB=PC.

You need to show that PAB=PAC.

Let us consider PAB and PAC. In these two triangles,

PB=PC (Given)

PBA=PCA=90 (Given)

PA=PA (Common side)

So, PABPAC (RHS rule)

So, PAB=PAC(CPCT)

721348_570019_ans_42f06bc0b1b4429a8799f1abb6c31c7b.png

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