Find the Length of a Tangent Drawn to a Circle with Radius 5cm, from a Point 13 Cm from the Center of the Circle. - Mathematics

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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.

Δ๐‘‚๐‘ƒ๐‘„ is right angled triangle, ∠OPQ = 90°

๐ต๐‘ฆ ๐‘๐‘ฆ๐‘กโ„Ž๐‘Ž๐‘”๐‘œ๐‘Ÿ๐‘Ž๐‘  ๐‘กโ„Ž๐‘’๐‘œ๐‘Ÿ๐‘’๐‘š, ๐‘‚๐‘„2 = ๐‘‚๐‘ƒ2 + ๐‘ƒ๐‘„2

⇒ 132 = 52 + ๐‘ƒ๐‘„2

⇒ ๐‘ƒ๐‘„2 = 169 − 25 = 144

⇒ PQ =` sqrt(144)` = 12๐‘๐‘š

Length of tangent = 12 cm

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Chapter 8: Circles - Exercise 8.2 [Page 33]

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RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 2 | Page 33

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