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(b)Explain why ∠= ∠OAPOPAand label them as angle x your copy of the diagram.on(c)Explain why ∠= ∠OBPOPBand label them as angle y your copy of the diagram.(d)Express ∠APBin terms ofx andony.ABPOABPQ1.4JNOKMLθβ
MEP Pupil Text - Additional Material:Mathematical Proof24(e)Use the sum of the angles in a triangle to explain why ∠=°-AOP1802and ∠=°-BOP1802y(f)Use the fact that ∠AOP,∠∠BOP and AOBare angles at a point to showthat ∠=+AOB22xy(g)Combine parts (d) and (f) to prove that ∠=× ∠AOBAPB211.O is the centre of the circle in thediagram opposite.M is the midpoint of the chord GH.Prove that OM is perpendicular to GH.(Hint: Join O to G, H and M.)Ox...1.4GHM