- Home
- Class 10
- Class 10 Maths
- Circles : THEOREM 1:

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.

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

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;

OQ_{1} > OP

OQ_{2} > OP

OQ_{3} > OP

OQ_{n} > OP

Since OP is the shortest line

Hence, OP ⊥ XY proved

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

To Prove: PQ = PR

Proof:

In Î” POQ and Î” POR

OQ = OR (radii)

PO = PO (common side)

∠PQO = ∠PRO (Right angle)

Hence; Î” POQ â‰ˆ Î” POR proved

- 10th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2015

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

Introduction
>
NCERT Solution - Exercise 3.1
>
NCERT Solution - Exercise 3.2 Part-1
>
NCERT Solution - Exercise 3.2 Part-2
>
NCERT Solution - Exercise 3.3 Part-1
>
NCERT Solution - Exercise 3.3 Part-2
>
NCERT Solution - Exercise 3.4 Part-1
>
NCERT Solution - Exercise 3.4 Part-2
>
NCERT Solution - Exercise 3.5 Part-1
>
NCERT Solution - Exercise 3.5 Part-2
>
NCERT Solution - Exercise 3.6 Part-1
>
NCERT Solution - Exercise 3.6 Part-2
>

NCERT Solution - Exercise 4.1 Part-1
>
NCERT Solution - Exercise 4.1 Part-2
>
NCERT Solution - Exercise 4.2 Part-1
>
NCERT Solution - Exercise 4.2 Part-2
>
NCERT Solution - Exercise 4.2 Part-3
>
NCERT Solution - Exercise 4.3 Part-1
>
NCERT Solution - Exercise 4.3 Part-2
>
NCERT Solution - Exercise 4.3 Part-3
>
NCERT Solution - Exercise 4.3 Part-4
>
NCERT Solution - Exercise 4.3 Part-5
>
NCERT Solution - Exercise 4.4 Part-1
>
NCERT Solution - Exercise 4.4 Part-2
>

Solution of Exercise 5.1 (NCERT)-Part-1
>
Solution of Exercise 5.1 (NCERT)-Part-2
>
Solution of Exercise 5.1 (NCERT)-Part-3.1
>
Solution of Exercise 5.1 (NCERT)-Part-3.2
>
Solution of Exercise 5.2 (NCERT) Part -1
>
Solution of Exercise 5.2 (NCERT) Part -2
>
Solution of Exercise 5.2 (NCERT) Part -3
>
Solution of Exercise 5.2 (NCERT) Part -4
>
Solution of Exercise 5.2 (NCERT) Part -5
>
Solution of Exercise 5.2 (NCERT) Part -6
>
Solution of Exercise 5.3 (NCERT)Part -1
>
Solution of Exercise 5.3 (NCERT)Part - 2
>
Solution of Exercise 5.3 (NCERT)Part - 3
>
Solution of Exercise 5.3 (NCERT)Part - 4
>
Solution of Exercise 5.3 (NCERT)Part - 5
>
Solution of Exercise 5.3 (NCERT)Part - 6
>
Solution of Exercise 5.3 (NCERT)Part - 7
>
Solution of Exercise 5.3 (NCERT)Part - 8
>
Solution of NCERT Exercise 5.4 (Optional)
>

Introduction : Theorems
>
NCERT Solution of Exercise 6.1
>
NCERT Solution Exercise 6.2 Part - I
>
NCERT Solution Exercise 6.2 Part - II
>
NCERT Solution Exercise 6.2 Part - III
>
NCERT Solution of Exercise 6.3 Part - III
>
NCERT Solution of Exercise 6.4
>
NCERT Solution of Exercise 6.5
>
NCERT Solution of Exercise 6.5 Part - 2
>
NCERT Solution of Exercise 6.6 - Part - 1
>
NCERT Solution of Exercise 6.6 - Part - 2
>

THEOREM 1:
>
Solution of NCERT Exercise 10.1
>
Solution of NCERT Exercise 10.2
>
Solution of NCERT Exercise 10.2 - Part 2
>
Solution of NCERT Exercise 10.2 - part - 3
>
Solution of NCERT Exercise 10.2 - part - 4
>
Solution of NCERT Exercise 10.2 - part - 5
>
Solution of NCERT Exercise 10.2 - part - 6
>