Question

Draw a line AB = 5 cm. Mark a paint C on AB such that AC = 3 cm. Using a ruler and a compass only, construct : 

(i) A circle of radius 2.5 cm, passing through A and C.

(ii) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Answer 1

Steps of construction :

(1) Draw a line AB = 5 cm.

(2) Mark a point C on AB such that AC = 3 cm.

(3) Draw a perpendicular bisector of AC.

(4) Mark a point O on perpendicular bisector from A of length 2.5 cm.

(5) Taking O as centre and OA as radius draw a circle, which is the required circle.

(6) Join O and B.

(7) Draw a circle with OB as diameter which cuts the given circle at points P and Q.

(8) Join PB and QB, which are the required tangents. QB = PB = 3 cm

Here, length of tangents is 3 cm.