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Diagram

Draw a circle with center O and radius 3 cm. Take the point P and the point Q at a distance of 7 cm from the center of the circle on the opposite side of the circle such that their line of intersection passing through the center of the circle Draw a tangent to the circle from the point P and the point Q

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#### Solution

**Steps of construction:**

- With centre O, draw a circle of radius 3 cm.
- Take point P and Q such that OP = 7 cm and OQ = 7 cm.
- Draw the perpendicular bisector of seg OP. It intersects OP in point M.
- Also, draw the perpendicular bisector of seg OQ. It intersects OQ in point N.
- With M as centre and radius equal to PM, draw an arc intersecting the circle in points R and with N as centre and radius equal to NQ, draw an arc intersecting the circle in points S.
- Draw rays PR and QS.

Rays PR and QS are the required tangents to the circle.

Concept: Construction of a Tangent to the Circle at a Point on the Circle

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