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area of polygon AQPBO does not change when points P,C move

Source: China Northern MO 2009 p6 CNMO

December 12, 2020
geometryfixedarea

Problem Statement

Given a minor sector AOBAOB (Here minor means that ∠AOB<90 \angle AOB <90). OO is the centre , chose a point CC on arc ABAB ,Let PP be a point on segment OCOC , join APAP , BPBP , draw a line through BB parallel to APAP , the line meet OCOC at point QQ ,join AQAQ . Prove that the area of polygon AQPBOAQPBO does not change when points P,CP,C move . https://cdn.artofproblemsolving.com/attachments/3/e/4bdd3a20fe1df3fce0719463b55ef93e8b5d7b.png
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