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

Answer 1

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 = $\frac{6}{2} = 3$
Now, in $ΔOTB, OT^2+TB^2 = OB^2$
$∴ r^2+3^2=(r+1)^2 ⇒ r=4$
$∴ D=2(R)=2(r+1)=10cm$
So, the correct answer is 10 cm.