Find the length of a tangent drawn to a circle with radius 5cm, from a point 13 cm from the center of the circle.
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
Video Tutorials For All Subjects
- Circles Examples and Solutions