# CAT 2020 Quant Question [Slot 2] with Solution 23

Question

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

Option: 10
Solution:

Given, $d + 2 = D \Rightarrow r + 1 = R$

In the figure $OT = r$ and $OB = r + 1$

$OT \bot AB$ as AB is the tangent

OT bisects AB i.e., $TB = \frac{6}{2} = 3$

Now, in $\Delta OTB,O{T^2} + T{B^2} = O{B^2}$

$\therefore {r^2} + {3^2} = {(r + 1)^2} \Rightarrow r = 4$

$\therefore D = 2(R) = 2(r + 1) = 10cm$

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