NCERT Solutions of Circles Class 10
<< NCERT Solution of Exercise 8.4 (Part - II)Solution of NCERT Exercise 10.1 >>

Circles

Tangent to a circle: A line which intersects a circle at any one point is called the tangent.

  • There is only one tangent at a point of the circle.
  • The tangent to a circle is perpendicular to the radius through the point of contact.
  • The lengths of the two tangents from an external point to a circle are equal.

THEOREM 1:

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Construction: Draw a circle with centre O. Draw a tangent XY which touches point P at the circle.

Class ten Math Circle Theorem 1

To Prove: OP is perpendicular to XY.

Draw a point Q on XY; other than O and join OQ. Here OQ is longer than the radius OP.

OQ > OP

For every point on the line XY other than O, like Q1, Q2, Q3, ....Qn;

OQ1 > OP

OQ2 > OP

OQ3 > OP

OQn > OP

Since OP is the shortest line

Hence, OP ⊥ XY proved

THEOREM 2:

The lengths of tangents drawn from an external point to a circle are equal.

Construction: Draw a circle with centre O. From a point P outside the circle, draw two tangents P and R.

Class ten Math Circle Theorem 2

To Prove: PQ = PR

Proof:

In ” POQ and ” POR

OQ = OR (radii)

PO = PO (common side)

PQO = PRO (Right angle)

Hence; ” POQ ‰ˆ ” POR proved


NCERT Solutions of Circles Class 10
<< NCERT Solution of Exercise 8.4 (Part - II)Solution of NCERT Exercise 10.1 >>

Circles will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.