Quantitative Aptitude Question on Triangles, Circles & Quadrilaterals

Question

Let $C_1$ and $C_2$ be concentric circles such that the diameter of $C_1$ is 2 cm longer than that of $C_2$ . If a chord of $C_1$ has length 6 cm and is a tangent to $C_2$ , then the diameter, in cm, of $C_1$ is
[This Question was asked as TITA]

Answer 1

Solution

Given, $d+2=D$
$⇒ r+1 = R$
In the figure $OT = r$ and $OB = r+1$
$OT ⊥ AB$ as $AB$ is the tangent
OT bisects AB i.e., $TB=\frac 62 = 3$
Now, in ΔOTB, $OT^2+TB^2 = OB^2$
∴ $r^2+32=(r+1)^2$
$⇒ r=4$
∴ $D=2(R)=2(r+1)=10$ cm

So, the correct option is (A): $10$ cm