Draw a circle of radius 6cm.from …

Given: A circle whose centre is O and radius is 6 cm and a point P is 10 cm away from its centre.
To construct: To construct the pair of tangents to the circle and measure their lengths.
 
Steps of Construction:

1. Join PO and bisect it. Let M be the mid-point of PO.
2. Taking M as centre and MO as radius, draw a circle. Let it intersects the given circle at the points Q and R.
3. Join PQ and PR.
   Then PQ and PR are the required two tangents.
   By measurement, PQ = PR = 8 cm
   Justification: Join OQ and OR.
   Since {tex}\angle QPO{/tex} and {tex}\angle ORP{/tex} are the angles in semicircles.
   {tex}\therefore \angle OQP = 90^\circ = \angle ORP{/tex} 
   Also, since OQ, OR are radii of the circle, PQ and PR will be the tangents to the circle at Q and R respectively.
   {tex}\therefore {/tex} We may see that the circle with OP as diameter increases the given circle in two points. Therefore, only two tangents can be draw.