InterviewSolution
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InterviewSolution
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In the adjoining figure, two circles with centres O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles. |
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Answer» Let the radius of the bigger circle be R and that of smaller circle be r. OA, OB, OC and OD are the radii of the bigger circle. ∴ OA = OB = OC = OD = R PQ = PA = r OQ + BQ = OB … [B – Q – O] OQ = OB – BQ = R – 9 OE + DE = OD ….[D – E – O] OE = OD – DE = [R – 5] As the chords QA and EF of the circle with centre P intersect in the interior of the circle, so by the property of internal division of two chords of a circle, OQ × OA = OE × OF ∴ (R – 9) × R = (R – 5) × (R – 5) …[∵ OE = OF] ∴ R2 – 9R = R2 – 10R + 25 ∴ -9R + 10R = 25 ∴ R = [25units] AQ = AB – BQ = 2r ….[B-Q-A] ∴ 2r = 50 – 9 = 41 ∴ r = 41/2 = 20.5 units |
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