# Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle

**Solution:**

Steps of construction:

Draw any circle using a bangle.

To find its centre:

- Draw two chords on the circle say AB and CD.
- Draw the perpendicular bisectors of AB and CD to intersect at O.

Now, ‘O’ is the centre of the circle (since the perpendiculars drawn from the centre of a circle to any chord bisect the chord and vice versa).

To draw the tangents from a point ‘P’ outside the circle.

- Take a point P outside the circle and draw the perpendicular bisector of OP which meets at OP at O’.
- With O’ as the centre and OO’ as radius draw a circle that cuts the given circle at Q and R.
- Join PQ and PR.

PQ and PR are the required tangents.

Proof:

∠QOP = ∠ORP = 90° (Angle in a semi-circle)

∴ OQ ⊥ QP and OR ⊥ RP.

Hence, we have PQ and PR as the tangents to the given circle.

**Video Solution:**

## Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle

### NCERT Solutions Class 10 Maths - Chapter 11 Exercise 11.2 Question 7:

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle

PQ and PR are the required tangents to the given circle