Q. 84.1( 9 Votes )

# I prove that, the two intersecting chords of any circle cannot bisect each other unless both of them are diameters of the circle.

Answer :

Given, AB and CD are Diameters.

To prove: OA = OB, OC = OD

Construction: Point D joined with B, Point A joined with C.

DAC = 90^{0} (Rectangle)

ACB = 90^{0} (Rectangle)

CBD = 90^{0} (Rectangle)

BDA = 90^{0} (Rectangle)

ACBD is Rectangle, So AD = CB, AD BCand BD = AC,BD AC

In OCB and ODA

OCB = ODA (Interior angles, BC AD)

BC = AD (Rectangle)

OBC = OAD (Interior angles, BC AD)

BCA SA Congruency

In OCB ODA

Hence Using CPCT, OA = OB, OD = OC

Hence Proved.

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