A circle with Centre O is drawn with diameter PQ and a chord PM. Another circle is drawn with OP as diameter to cut PM at N. prove that MQ = 2 ON
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consider ∆PON and ∆PQM
1) <NPO = <MPQ (common angle)
2) <PNO = <PMQ
therefore ∆PON ~ ∆PQM (AA test)
therefore NO/MQ = PO/PQ (ratios of corresponding sides of similar triangles are equal)
therefore NO/MQ = ½ (2radius = diameter)
therefore 2NO = MQ
1) <NPO = <MPQ (common angle)
2) <PNO = <PMQ
therefore ∆PON ~ ∆PQM (AA test)
therefore NO/MQ = PO/PQ (ratios of corresponding sides of similar triangles are equal)
therefore NO/MQ = ½ (2radius = diameter)
therefore 2NO = MQ
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