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CBSE Class 9 Answered

The two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection. Prove that the chords are equal.
Asked by Topperlearning User | 07 Feb, 2014, 12:33: PM
answered-by-expert Expert Answer

Draw OM AB and ON CD

MOP = 180o - 90o - MPO

= 90o - MPO

= 90o - NPO

= NOP

In OMP and ONP,

OMP = ONP = 90o (by construction)

MOP = NOP (shown above)

OP = OP (common)

Chords AB and CD are equidistant from centre O.

Therefore, AB = CD

(Chords which are equidistant from the centre are equal)

Answered by | 07 Feb, 2014, 02:33: PM

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