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Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Answer:

**Solution:**

A circle's tangent is a single-pointed line that intersects the circle. The "point of tangency" is the location where the circle and the tangent cross. The radius of the circle, with which it crosses, is perpendicular to the tangent.

Steps to construct:

Step 1: Consider a point O on a line, with center O, and radius 3cm, draw a circle.

Step 2: Extend its diameters on both sides and cut off OP = OQ = 7cm.

Step 3: Mark the mid-points of OP and OQ as M and N respectively.

Step 4: With Centers M and N and OP and OQ as diameters, draw circles which intersect the given circle at A, B and C, D respectively.

Step 5: Join PA, PB, QC, QD. Hence, PA, PB and QC, QD are the required tangents.

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