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प्रश्न
In figure OQ : PQ = 3 : 4 and perimeter of ΔPDQ = 60cm. determine PQ, QR and OP.
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उत्तर
Given OQ: PQ = 3 : 4
Let OQ = 3x PQ = 4x
OP = y
∠OQP = 90° [since at point of contact, tangent is perpendicular to radius]
In ΔOQP, by Pythagoras theorem
𝑂𝑃2 = 𝑂𝑄2 + 𝑄𝑃2
⇒ 𝑦2 = (3𝑥)2 + (4𝑥)2
⇒ 𝑦2 = 9𝑥2 + 16𝑥2 = 25𝑥2
⇒ 𝑦 = `sqrt(25x^2)` = 5𝑥
Perimeter = OQ + PQ + OP = 3x + 4x + 5x = 12x
According to problem perimeter = 60
∴ 12x = 60
x =`60/12`
= 5𝑐𝑚
OQ = 3 × 5 = 15𝑐𝑚
PQ = 4 × 5 = 20 𝑐𝑚
OP = 5 × 5 = 25𝑐𝑚
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