Page 3 - Lesson Notes-Introduction Ch-10 (Circles)

Number of Tangents from a Point on a Circle

1. There could be only one tangent at one point of contact.

2. Tangent could not be drawn from any point inside the circle.

3. There could be only two tangents to a circle from any point outside the circle.

Theorem 10.1- The tangent at any point of a circle is perpendicular to the

radius through the point of contact.

Proof- Referring to the figure:

OA=OC (Radii of circle)

Now OB=OC+BC

∴OB>OC (OC being radius and B any point on tangent)

⇒OA<OB

B is an arbitrary point on the tangent.

Thus, OA is shorter than any other line segment joining O to any

point on tangent.

Shortest distance of a point from a given line is the perpendicular distance from that
line.

Hence, the tangent at any point of circle is perpendicular to the radius.

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