Question
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Solution
Fig.
Steps of Construction :
(i) Construct a circle of radius 6 cm.
(ii) Join PO and bisect it Let M be the midpoint of PO.
(iii) Taking M as centre and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.
(iv) Join PQ and PR.
(v) PQ and PR are the required two tangents.
(vi) PQ = PR = 8 cm.
Justification :
Join OQ and OR.
∵ ∠OQP and ∠ORP are the angles in semi circles.
∠OQP = 90° = ∠ORP
Also, since OQ, OR are radii of the circle, PQ and PR will be the tangents to the circle at Q and R respectively.
