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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.
Solution
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.
Δ๐๐๐ is right angled triangle, ∠OPQ = 90°
๐ต๐ฆ ๐๐ฆ๐กโ๐๐๐๐๐๐ ๐กโ๐๐๐๐๐, ๐๐2 = ๐๐2 + ๐๐2
⇒ 132 = 52 + ๐๐2
⇒ ๐๐2 = 169 − 25 = 144
⇒ PQ =` sqrt(144)` = 12๐๐
Length of tangent = 12 cm
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