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Showing 1 question for Class 10. Tap a card to reveal the answer.

MathematicsCirclesmedium

A point P is 13 cm from the centre of a circle of radius 5 cm. Find the length of the tangent drawn from P to the circle.

Reveal answer ↓

What it is

A tangent touches a circle at one point and is perpendicular to the radius at that point.

Answer

The tangent is perpendicular to the radius at the point of contact, so the radius, tangent and line OP form a right-angled triangle with OP as the hypotenuse. Length of tangent = sqrt[OP^2 - r^2] = sqrt[13^2 - 5^2] = sqrt[169 - 25] = sqrt[144] = 12 cm.

tangent length = sqrt[OP^2 - r^2]

  • •Tangent is perpendicular to radius at contact
  • •Right triangle: OP hypotenuse
  • •Length = sqrt[13^2 - 5^2] = 12 cm

Why learn this

It's used in gear design, road curves and belt-and-pulley engineering.

💡 Memory trick

Radius, tangent and line to the point form a right triangle: tangent = sqrt(OP^2 - r^2).