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प्रश्न
In fig., AB and DC are two chords of a circle with centre O. these chords when produced meet at P. if PB = Bern, BA = 7cm and PO = 14.5cm, find the radius of the circle.
उत्तर
Let OD = OC = r (say)
PO = 14.5 , CP = r + 14.5
PD = 14.5 - r
In Δ BPD and Δ APC
∠ BPD = ∠ APC {Common)
∠ ABD + ∠ DBP = 180° ---(1) ( Linear pair )
Also, ∠ ABD + ∠ ACD = 180° ---(2} {Opposite angles of a cyclic quadrilateral)
From (1) and {2}
∠ DBP = ∠ ACD
∴ Δ BPD ~ Δ CPA {AA corollary)
`8/("r" + 14.5) = (4.5 - "r")/15`
120° = 14.52 - r2
r2 = 210.25- 120
r2 = 90.25
r = 9.50
Radius of the circle is 9.5cm .
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