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In the given figure, O is …

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In the given figure, O is the centre of a circle of radius r cm, OP and OQ are perpendicular to AB and CD respectivAN ely and PQ=1 cm. If AB||CD, AB=6 cm, and CD=8 cm, determine r.

Posted by Abhishek Kayal 8 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Shweta Gulati 8 years, 9 months ago

Join OA and OC

As perpendicular drawn from the center, bisects the chord AB and CD at P and Q respectively.
AP = PB = ½ AB = 3 cm
And CQ = QD = ½ CD = 4 cm
In right triangle OAP, by Pythagorean theorem
OA ² = OP ² + AP ²
5 ² = OP ² + 3 ²
⇒ OP ² = 5 ² - 3 ²
⇒ OP ² = 25 – 9 = 16
⇒ OP = 4 cm
In right triangle OCQ, by Pythagorean theorem
OC ² = OQ ² + CQ ²
⇒ 5 ² = OQ ² - 4 ² = 9
⇒ OQ = 3
∴ PQ = PO – QO
PQ = 4 -3
PQ = 1 cm.

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