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605-655 (Medium)|   Geometry|      
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WarriorWithin
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Line AB is tangent to the inner of the two concentric circles at point 18 Dec 2020, 10:37
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45% (medium)

Question Stats:

65% (01:53) correct 35% (01:21) wrong based on 46 sessions

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Line AB is tangent to the inner of the two concentric circles at point C. Points A and B lie on the outer circle. Radii of both the circles are integers. If AB = 6 cm, the length of radius of outer circle is

A. 2
B. 3
C. 4
D. 5
E. 6
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D
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Line AB is tangent to the inner of the two concentric circles at point 18 Dec 2020, 13:11
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WarriorWithin
Line AB is tangent to the inner of the two concentric circles at point C. Points A and B lie on the outer circle. Radii of both the circles are integers. If AB = 6 cm, the length of radius of outer circle is

A. 2
B. 3
C. 4
D. 5
E. 6
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Please refer to the diagram below.

AB is a chord in the larger circle and also a tangent to the snaller circle. The radius, and the tangent are at 90 degrees.

Also, the perpendicular from the center to the chord bisects chord AB, Therefore AC = CB = 3

In OCB, OB is the radius of the larger circle, which is also the hypotenuse and BC is the radius of the smaller circle.

Since both are integers, there are part of the pythagoras triplet 3, 4, 5.

Therefore the radius of the larger circle = 5


Option D

Arun Kumar
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Line AB is tangent to the inner of the two concentric circles at point 10 Apr 2023, 15:08
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