Q1
A tangent to a circle is:
Aperpendicular to the radius at the point of contact
Bparallel to the radius
Cpassing through the centre
Dalways a chord
CBSEClass 10 (CBSE)MathematicsCh 10 · Topic 1
Tangent to a Circle
Learning the key property of a tangent line to a circle.
Core concept
This perpendicularity property is fundamental to solving many circle-related problems — for example, if a tangent is drawn from an external point to a circle, the length of this tangent can be calculated using the Pythagoras theorem, since the radius, tangent, and the line from the external point to the centre form a right triangle. For a tangent length of unknown value, radius 5cm, and distance from external point to centre 13cm: tangent² + 5² = 13², giving tangent = 12cm.
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• A tangent touches a circle at exactly one point, without entering its interior.
• A tangent is always perpendicular to the radius at the point of contact.
• This perpendicularity creates a right triangle, solvable using the Pythagoras theorem.
• Example: radius 5cm, external distance 13cm, gives tangent length 12cm.