Question

In the given figure, if OC $=$ 9 cm and OB $=$ 15 cm, then BC $+$ BD is equal to:

• A. 18 cm
• B. 12 cm
• C. 24 cm
• D. 36 cm

Answer 1

Answer: (C)

24 cm

We know that, a tangent to a circle is perpendicular to the radius at the point of contact.

So, $△OCB$ is right a triangle, right angled at $C$.

Hence, by Pythagoras' theorem, we have:

$B{C}^2=O{B}^2-O{C}^2$

$\Rightarrow B{C}^2=225-81=144$

$\therefore BC=12cm$.

We also know that, the tangents drawn from the same external point to a circle are equal.

Since $BC$ and $BD$ are tangents drawn from the same external point, $B$, we have:

$BC=BD=12cm$.

So, $BC+BD=24cm$.

Hence, $BC+BD=24cm$.