Let Γ be a circle with centre O. Let A be the another circle passing through O and intersecting Γ at points A and B. A diameter CD of Γ intersects A at point P different from O. Prove that ∠APC = ∠BPD.
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Let Γ be a circle with centre O. Let A be the another circle passing through O and intersecting Γ at points A and B. A diameter CD of Γ intersects A at point P different from O. Prove that ∠APC = ∠BPD.
Let Γ be a circle with centre O. Let A be the another circle passing through O and intersecting Γ at points A and B. A diameter CD of Γ intersects A at point P different from O. Prove that ∠APC = ∠BPD.
Suppose that A’ is a point on A such that ∠A’PC = ∠BPD. Then the segments OA’ and OB subtends same angle in the respective minor arcs, so OA’ = OB. This shows that A lies on Γ and hence A’ =A.
This proves that ∠APC = ∠BPD.