The adjoining figure shows a circle with centre O in which a diameter AB bisects the chord PQ at point R. If PR = RQ = 8 cm and RB = 4 cm, find the radius of the circle.
Circles
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Question

The adjoining figure shows a circle with centre O in which a diameter AB bisects the chord PQ at point R. If PR = RQ = 8 cm and RB = 4 cm, find the radius of the circle.

KnowledgeBoat · Accepted Answer

Join OQ. Radius = OQ = OB = x (let) ⇒ OR = OB - RB = (x - 4) cm. We know that, A straight line drawn from the center of a circle to bisect a chord, is perpendicular to the chord. Since, PR = QR, thus R is mid-point of PQ. ∴ OR ⊥ PQ In right-angled triangle OQR, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OQ2 = OR2 + QR2 ⇒ x2 = (x - 4)2 + 82 ⇒ x2 = x2 + 42 - 2 × x × 4 + 64 ⇒ x2 = x2 + 16 - 8x + 64 ⇒ x2 - x2 + 8x = 80 ⇒ 8x = 80 ⇒ x = = 10 cm. Hence, radius of circle = 10 cm.

Mathematics

The adjoining figure shows a circle with centre O in which a diameter AB bisects the chord PQ at point R. If PR = RQ = 8 cm and RB = 4 cm, find the radius of the circle.

Circles

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