b Explain why OAP OPA and label them as angle x on your copy of the diagram c

B explain why oap opa and label them as angle x on

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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 and on y. ABPO A B P Q 1.4 JNOKMLθβ
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MEP Pupil Text - Additional Material: Mathematical Proof 24 (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.)O x . . . 1.4 G H M
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