CBSE Class 10 Maths Notes Chapter 10 Circles
Circle: A circle is a collection of all points in a plane which are at a constant distance from a fixed point.
Centre: The fixed point is called the centre.
Radius: The constant distance from the centre is called the radius.
Properties of Tangent to Circle
Theorem 1: Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Given: XY is a tangent at point P to the circle with centre O.
To prove: OP ⊥ XY
Construction: Take a point Q on XY other than P and join OQ
Proof: If point Q lies inside the circle, then XY will become a secant and not a tangent to the circle
OQ > OP
This shows that AB meets the circle at point P.
Hence, AP is tangent to the circle at P.
Theorem 3: Prove that the lengths of tangents drawn from an external point to a circle are equal
Given: PT and PS are tangents from an external point P to the circle with centre O.
To prove: PT = PS
Construction: Join O to P, T and S.
