From the below figure, if OC=9 cm and OB=15 cm, then BC+BD = ___.

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

So, $∆\mathrm{OCB}$ is a right-angle triangle, right-angled at C.

Hence, by Pythagoras' theorem: BC² = OB² - OC²

Given, OC = 9 cm and OB = 15 cm

BC² = 15² - 9²

BC² = 225 - 81 = 144

BC = 12 cm.

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

i.e., BC = BD = 12 cm.

Therefore, BC + BD = 24 cm.