Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm 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

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Question :

Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm 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

Started 10 months ago by Shashank in

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Answer : 10

Explanatory Answer

In the figure, ‘O’ is the centre of circles ‘C1’ and ‘C2’ with radii ‘ x ’ & ‘ y ’ respectively
If d1 – d2 = 2cm, x - y = 1cm
Hence, MB = 1cm
AB is a chord with 6cm length and tangent to C2.
Therefore, AN = NB = 3cm ; ON = y; OB = y + 1
In right triangle ONB:
(ON) 2 + (NB) 2 = (OB) 2
y 2 + 9 = (y+1) 2
9 = 2y + 1
2y + 8
y = 4
Therefore, x = y + 1 = 5cm
Diameter = 2x = 10cm