Question

In figure, there are two concentric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Answer 1

OA = 5 cm

OB = 3 cm

AP = 12 cm

BP = ?

We know that

At the point of contact, radius is perpendicular to tangent.

For circle 1, ΔOAP is right triangle

By Pythagoras theorem, 𝑂𝑃² = 𝑂𝐴² + 𝐴𝑃²

⇒ 𝑂𝑃² = 5² + 12² = 25 + 144

= 169

⇒ OP = `sqrt(169)` = 13 𝑐𝑚

For circle 2, ΔOBP is right triangle by Pythagoras theorem,

𝑂𝑃² = 𝑂𝐵² + 𝐵𝑃²

13² = 3² + 𝐵𝑃²

𝐵𝑃² = 169 − 9 = 160

𝐵𝑃 = `sqrt(160) = 4sqrt(10)` 𝑐𝑚