# Circles Exercise 10.5 – Class 10

## Circles Exercise 10.5 – Questions:

1. Draw a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents.
2. Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the circle.
3. Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it.
4. Draw a pair of perpendicular tangents of length 5 cm to a circle.
5. Construct tangents to two concentric circles of radii 2 cm and 4 cm from a point 8 cm away from the centre.

## Circles Exercise 10.5 – Solutions:

1. Draw a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents.

Solution: Lent of the tangents, t = √(d2 – r2)

Length of the tangents, t = √(102 – 62) = √(100 – 36) =  √64  = 8 cm

1. Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the circle.

Solution: 1. Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it.

Solution: 1. Draw a pair of perpendicular tangents of length 5 cm to a circle.

Solution: 1. Construct tangents to two concentric circles of radii 2 cm and 4 cm from a point 8 cm away from the centre.

Solution: 