# Ex.11.2 Q7 Constructions Solution - NCERT Maths Class 10

## Question

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.

## Text Solution

**Steps:**

**Steps of construction:**

**(i)** Draw any circle using a bangle.

To find its centre

**(a)** Draw any two chords of the circle say \(AB\) and \(CD\)*.*

**(b)** Draw the perpendicular bisectors of \(AB\) and \(CD\) to intersect at \(O\).

Now, \(‘O’\) is the centre of this 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.

**(ii)** Take any point \(P\) outside the circle and draw the perpendicular bisector of \(OP\) which meets at \(OP\) at \(O’\).

**(iii)** With \(O’\) as center and \(OO’\) as radius draw a circle which cuts the given circle at \(Q\) and \(R\).

**(iv)** Join \(PQ\) and \(PR\).

\(PQ\) and \(PR\) are the required tangents.

**Proof:**

**\(\angle {\rm{OQP}} = \angle {\rm{ORP}} = 90^\circ \)** (Angle in a semi \(-\) circle)

\(\therefore \,{OQ} \,\bot\, {QP}\) and \({OR}\, \bot\, {RP}\)

Hence, \(PQ\) and \(PR\) are the tangents to the given circle.