Question

Find the length of a tangent drawn to a circle with radius 5cm, from a point 13 cm from the center of the circle.

Answer 1

Consider a circle with center O.

OP = radius = 5 cm.

A tangent is drawn at point P, such that line through O intersects it at Q, OB = 13cm.

Length of tangent PQ = ?

A + P, we know that tangent and radius are perpendicular.

Δ𝑂𝑃𝑄 is right angled triangle, ∠OPQ = 90°

𝐵𝑦 𝑝𝑦𝑡ℎ𝑎𝑔𝑜𝑟𝑎𝑠 𝑡ℎ𝑒𝑜𝑟𝑒𝑚, 𝑂𝑄² = 𝑂𝑃² + 𝑃𝑄²

⇒ 13² = 5² + 𝑃𝑄²

⇒ 𝑃𝑄² = 169 − 25 = 144

⇒ PQ =` sqrt(144)` = 12𝑐𝑚

Length of tangent = 12 cm