## Circles Exercise 10.5 – Questions:

- 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.
- Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the circle.
- Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it.
- Draw a pair of perpendicular tangents of length 5 cm to a circle.
- 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:

**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 = √(d^{2} – r^{2})

Length of the tangents, t = √(10^{2} – 6^{2}) = √(100 – 36) = √64 = 8 cm

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

Solution:

**Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it.**

Solution:

**Draw a pair of perpendicular tangents of length 5 cm to a circle.**

Solution:

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

Solution: