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Question


Perpendicular bisectors of two sides of the triangle intersect each other at a point on the third side. Then show that the triangle is right angled triangle. (3.74)


Solution

Construction : Draw a right-angled ABC and name the point on AC, P.Join PB.Draw a circle circumscribing the triangle.By perpendicula- bisector theorem,PA = PB and PB = PC   Or, PA = PB  =PC In the circle, with PA = PB =PC as radii, P becomes the centre.We know that angle in a semicircle is 90°.  Thus, ABC = 90°.Hence proved.


Mathematics
Mathematics (Geometry)
Standard IX

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