Question

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. Construct tangents to the circle from these two points P and Q.
 

Answer 1

Steps of constructions:

Step 1: draw a circle of radius 3 cm whose centre is O.

Step 2: P and Q are points on one of extended diameter of circle such that OP = OQ  = 7 cm.

Step 3: Draw perpendicular bisectors on line segments OP and OQ which intersects them at O₁ and O₂ respectively.

Step 4: Take O₁ & O₂ as centre and draw circles C₁ & C₂ of radius 

O₁P  = O₂Q = \(\frac72\) cm

Let circle C₁ intersect the original circle at points A and B & circle C₂ intersect original circle at point C and D.

Step 5: Join PA, PB & CQ, DQ which are required tangents to circle from points P & Q 7cm away from the centre O.