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Question

In the fig. 3.76 the point P is in the interior of ABC, such that ray BP is the angle bisector of ABC but ray CP is not an angle bisector of ACB. Then prove that the ray AP is not angle bisector of BAC.


Solution


Given : BP is the angle bisector of ABC, butCP is not the angle bisector of ACB.Thus, by angle-bisector theorem,P is equidistant from AB and AC.Or, PX = PZ  ...(i)And P is not equidistant from AC and BC.Or, PZ  PY   ......(ii)From (i) and (ii), we get :PX PYOr, P is not equidistant from AB and AC.Or, AP is not an angle bisector of BAC.Hence proved.

Mathematics
Mathematics (Geometry)
Standard IX

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