Ex.11.2 Q7 Constructions Solution - NCERT Maths Class 10

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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.

  
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