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प्रश्न
If AB and CD are two chords which when produced meet at P and if AP = CP, show that AB = CD.
उत्तर
Here, chord AB and CD of the circle intersect at P.
∴ PA x PB = PC x PD
⇒ PB = `("PC" xx "PD")/"PA"`
⇒ PB = `("AP" xx "PD")/"AP"` ...( ∵ PC = AP(Given))
⇒ PB = PD ...(i)
Now, AB = AP - BP
⇒ AB = CP - PD ...(∵AP = CP(Given), BP = PD(from (i)))
AB = CD
Hence, AB = CD
Hence proved.
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