In $∆$ ABC, (fig. 3.75) the perpendicular bisectors of side AB and AC intersect each other at point P. Show that the perpendicular bisector of CB also passes through point P.

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Solution

$Construction : Draw a perpedicular bisector of CB, l_{3} . Since l_{1} and l_{2} are perpendicular bisectors of AB and AC, PA = PB (perpendicular - bisector theorem) Also, PA = PC (perpendicular - bisector theorem) Thus, PA = PB = PC Or we can say that the perpendicular bisector of CB also passes through point P . Or, l passes through point P . Hence p roved .$

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In ∆ABC, (fig. 3.75) the perpendicular bisectors of side AB and AC intersect each other at point P. Show that the perpendicular bisector of CB also passes through point P.

In $∆$ ABC, (fig. 3.75) the perpendicular bisectors of side AB and AC intersect each other at point P. Show that the perpendicular bisector of CB also passes through point P.