Question

Draw a circle of radius 3.2. Take a point p at a distance of 6cm from the center of the circle. Without using the center of the circle, draw two tangents of the circle from point p

Answer 1

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1. Draw a circle with radius = 3.2cm.
2. Draw a diameter BA such that OA is radius.
3. Mark a point P outside the circle at a distance of 6cm from the centre of the circle.
4. Draw PR such that AP = PR .
5. Draw the perpendicular bisector of BR.
6. Taking MR as radius and M as radius draw a semicircle .
7. Construct 90° on P which will intersect the semicircle at a point Q.
8. Now taking PQ as radius and P as centre cut two arcs on the circle at X and Y respectively.
9. Hence we get the required two tangents XP and YP respectively.

Answer 2

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1) Draw a line segment 3.2 cm .

2) Take a point “p” at a distance of 6cm from the center and draw a secant PAB, intersecting the Circle at “A” and “B” .

3) Produce AP to C such that AP = CP .

4) Draw a semi-circle with CB as diameter .

5) Draw “PD” perpendicular “CB”, intersecting the semi-circle at D .

6) With P as a center and PD as radius draw arcs to intersect the given Circle at T and T' .

7) Join PT and PT' . Then PT and PT' are the required tangents .

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