CBSE Class 10 Mathematics Circles Worksheet Set F

CBSE Class 10 Circles (6). Students can download these worksheets and practice them. This will help them to get better marks in examinations. Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

CIRCLES

Key Points

1. Circle: A circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre).

2. Secant & Tangent to a Circle: In fig. 1 the line PQ and the circle have no common point. Line PQ is called non-intersecting. In fig. 2 line PQ a secant to a circle. In fig. 3, there is only 1 point A, which is common to the line PQ and the circle. The line is called a tangent to the circle.

3. Tangent to a Circle :

It is a line that intersects the circle at only one point. There is only one tangent at a point of the circle. The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.

4. Theorems :

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

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

5. Number of tangents from a point on a circle-

(i)There is no tangent to a circle passing through a point lying inside the circle.

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

(iii)There are exactly two tangents to a circle through a point lying outside the circle.

LEVEL I

1. In the given fig. O is the centre of the circle and PQ is tangent then POQ + QPO is equal to

2. If PQ is a tangent to a circle of radius 5cm and PQ = 12 cm, Q is point of contact, then OP is

3. In the given fig. PQ and PR are tangents to the circle, QOP = 70°, thenQPR is equal to

P a g e 86 | 118

4. In the given fig. QS is a tangent to the circle, OS = 8 cm, OQ = 6 cm then the length of QS is

5. In the given fig PQ is tangent to outer circle and PR is tangent to inner circle. If PQ = 4 cm, OQ = 3 cm and OR = 2 cm then the length of PR is

6. In the given fig. P, Q and R are the points of contact. If AB = 4 cm, BP = 2 cm then the perimeter of ABC is

7. The distance between two tangent parallel to each other to a circle is 12 cm. The radius of circle is

8. The chord of a circle of radius 10cm subtends a right angle at its centre.Find the length of the chord.

9. How many tangents can a circle have?

Please click the link below to download CBSE Class 10 Circles (6)