CIRCLE
CIRCLE
This content is part of NCERT Solutions for Class 10 Maths Chapter 10 Circles
A circle is the locus of a points which moves in a plane in such a way that its distance from a fixed point
remains constant.
9.2 SECANT AND TANGENT :
Secant to a circle is a line which intersects the circle in two distinct points.
A tangent to a circle is a line that intersects the circle in exactly one point.
9.3 THEOREM :
Statement : A tangent to a circle i perpendicular to the radius through the point of contact.
Given : A circle C (O, r) and a tangent AB at a point P.
To prove : OP AB
Construction : Take any points Q, other than P on the tangent AB. Join OQ. Suppose OQ meets the circle at R.
Proof: Among all line segments joining the point O to a point on AB, the shorted one is perpendicular to
AB. So, to prove that OP AB, it is sufficient to prove that OP is shorter than any other segment
joining O to any point of AB.
Clearly OP = OR
Now, OQ OR + RQ
OQ > OR
OQ > OP (OP = OR)
Thus, OP is shorter than any other segment joining O to any point of AB.














