Problem 23
Let AB and PQ be any two chords of a circle, intersecting at O. Tangents are drawn at P and Q, meeting AB extended at C and D respectively. Then, show that:
1/OA – 1/OC = 1/OB – 1/OD
Here’s a simulation that demonstrates the problem.
Try dragging the points A, B, P and Q. Is 1/OA – 1/OC always equal to 1/OB – 1/OD? How can we prove the same?
Solution
Alternate Segment Theorem
[coming soon]
Sine Rule
[coming soon]
Were you able to solve it using the above hints? Or, did you solve using any other method? Or, do you need some more help? You can reach out at the Telegram group.
Problem Source: CutTheKnot
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