NCERT Solutions for class 10 Maths Chapter 10 exercise 10.2 & 10.1 of Circles in Hindi Medium (प्रश्नावली 10.1 & प्रश्नावली 10.2) and English Medium for UP Board as well as CBSE Board 2018-19 onward download in PDF form. Click here to download * NCERT Boos* of Maths and all other subjects. Previous year questions from

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## NCERT Solutions for class 10 Maths Chapter 10

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### Class 10 Maths solutions – Circles

#### English Medium

#### Previous Years Questions

##### One mark questions

- Prove that tangents drawn at the ends of a diameter of a circle are parallel to each other. [CBSE 2017]

##### Two marks questions

- In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3cm, then find PC + PD. [CBSE 2017]

##### Three marks questions

- Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angle PTQ = 2 (angle OPQ). [CBSE 2017]

##### Four marks questions

- Prove that the lengths of tangents drawn from an external point to a circle are equal. [CBSE 2017]

#### More about Circles and its tangents

**Circle**: A circle is the set of points in a plane which are at the same distance from a fixed point in the plane. The fixed point is called the centre of the circle and the line segment joining the centre & a point on circle is called radius.**Tangent to a circle**: If a line drawn in the plane of a circle intersects the circle in one and only one point, then the line is called a tangent to the circle and the point at which the line intersect the circle is called the point of contact of the line with the circle.**Theorems on tangent to a circle**: (i). A tangent to a circle is perpendicular to the radius drawn from point of contact or A line drawn perpendicular to a radius at its end point on the circle is a tangent to the circle. (ii). the tangents drawn to a circle from a point in the exterior of the circle are equal in length or the lengths of tangents drawn from an external point to a circle are equal.**Number of tangents to a circle**: There are the following cases:

*There is no tangent to a circle passing through a point lying inside the circle.*

*There is one and only one tangent to a circle passing through a point lying on the circle.*

*There are exactly two tangents to a circle through a point lying outside the circle.*

**Historical Facts!**

- The circle is the most primitive and rudimentary of all human inventions. It is the corner stone in the foundation of science and technology. It is the basic tool used by greatest artists and architects in the history of mankind.
- The ancient Indian symbol of a circle, with a dot in the middle, known as ‘BINDU’ was probably instrumental in the use of circle as a representation of the concept zero.
- The ratio of the circumference of a circle to its diameter is always a constant. This constant is universally denoted by Greek letter π .