CAT 2020 Question Paper (Slot 2) Question 65

Question 65

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 6cm and is a tangent to C2, then the diameter, in cm, of C1 is

Correct Answer: 10


Now we know that the perpendicular from the centre to a chord bisects the chord. Hence at the point of intersection of tangent, the chord will be divided into two parts of 3 cm each. As you can clearly see in the diagram, a right angled triangle is formed there.

Hence   $$\left(r+1\right)^2=r^2+9$$ or $$r^{2\ }+1+2r\ =\ r^2+9\ or\ 2r=8\ or\ r=4cm$$

Hence the radius of the larger circle is 5cm and diameter is 10cm.

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