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

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#### 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, ๐๐^{2} = ๐๐^{2} + ๐๐^{2}

⇒ 13^{2} = 5^{2} + ๐๐^{2}

⇒ ๐๐^{2} = 169 − 25 = 144

⇒ PQ =` sqrt(144)` = 12๐๐

Length of tangent = 12 cm

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