Question
It two equal chords of a circle intersect within the circle. Prove that the line joining the point of intersection to the centre makes equal angles with the chords.
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Text solutionVerified
Let us consider a circle with centre and and be the chords which intersect at
According to the question, .
We need to prove
Drop perpendiculars and on and respectively and join .
In triangles and ,
(equal chords of a circle are equidistant from the centre)
(common side)
(both equal to )
By RHS criterion of congruence,
(by C.P.C.T.)
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Question Text | It two equal chords of a circle intersect within the circle. Prove that the line joining the point of intersection to the centre makes equal angles with the chords. |
Answer Type | Text solution:1 |
Upvotes | 150 |