Question

Draw a circle at a radius of 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.

Answer 1

Steps of Construction:
(i) Draw a chord PQ through the given point on the circle.

(ii) Take a point R on the circle and join P and Q to a point R.

(iii) Construct ∠ QPY = ∠ PRQ on the opposite sides of the chord PQ.

(iv) Produce YP to X' to get YPX as the required tangent.

Construct a tangent to the circle from an external point:
In this section we shall study the construction at tangent to a circle from an external point when its center is; (i) Know (ii) Unknown

Type (I). Construction at tangent to a circle from an external point when its centre is known.

Steps of Construction:
(i) Join the centre O of the circle to the given external point P i.e., join OP.

(ii) Draw right bisector of OP, intersecting OP at Q.

(iii) Taking Q as centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T'.

(iv) Join PT and PT' to get the required tangents as PT and PT'.