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Author’s Solution for Challenging Problems in Circles

1. Question:

AB & CD are two chords of a circle with centre ‘O’ intersecting each other at right angles. Prove that ∠AOC + ∠BOD = 180

[ Here, is an interesting story behind the problem. This problem was given to our author as an assignment when he was at his SSLC. The teacher has given instruction to do this problem using the theorem ‘The angle made by a chord at the centre is twice the angle at the circumference’ but instead our author has solved this problem in the other way which is beyond his level. Though the teacher initially got angry on looking at the solution (as our author didn’t apply the theorem taught to him), at last he appreciated our author for solving the problem the other way though it is complicated.]
The Teacher’s expected solution is also given below.


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