Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 is
Explanation:
The following figure can be drawn from the information given in the question.
Perpendicular OA will bisect the chord, hence AB = 3.
Let the radius of smaller circle be r, hence radius of bigger circle will be r + 1.
In right triangle OAB,
OB2 = OA2 + AB2
⇒ (r + 1)2 = r2 + 32
∴ r = 4
Diameter of C1 (the bigger circle) = 2(r + 1) = 10 cm.
Hence, 10.
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