Q. 35.0( 1 Vote )

Rita draws a right angled triangle. Let us prove logically that the perpendicular bisectors of sides are concurrent and where the position of the circum centre (inside/outside/on the side) is

Answer :

1.JPG


PO is perpendicular to AB and OQ is perpendicular to BC


Since Δ ABC is right angled at B so POQB forms a rectangle


Hence we can say that


PO = BQ (Opposite sides of rectangle)


BP = QO(Opposite sides of a rectangle)


In Δ AOP and Δ QOC


APO = OQC (OP and OQ are perpendiculars)


OAP = COQ (Corresponding angles)


PO = BQ = CQ (Q is midpoint of BC)


So Δ AOP and Δ COQ are congruent by A.A.S. axiom of congruency


Hence AO = OC


So O is the midpoint of AC


Hence the perpendiculars are concurrent


The circum centre lies on the midpoint of the hypotenuse of the triangle.


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