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