Question

Draw a line segment AB of length 8cm. Taking A as centre, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3cm. Construct tangents to each circle from the centre of the other circle.

Answer 1

Hint: Here we will proceed by constructing a line segment of given measurement. Also with both the radius given we will draw two circles such that they intersected by a new circle formed. Further we will join the intersected points which will form the required tangents.

Complete step-by-step answer:

Steps of construction-
 (1) A line segment AB of 8cm is drawn.

(2) With A as centre and radius equal to 4cm, a circle is drawn.
(3) With B as centre and radius equal to 3cm, a circle is drawn.

Now we need to draw tangent from point A to the right circle, and from point B to the left circle. To draw tangents to the right circle, we need to draw a perpendicular bisector of line AB.
(4) Make a perpendicular bisector of AB. Let M be the mid-point of AB.

(5) Taking M as centre and MA as radius, draw a circle.

(6) Let the middle circle intersect the left circle at P, Q and right circle at R, S.
(7) Join BP, BQ, AR and AS.

(8) Thus BP, BQ, AR and AS are the required tangents.

Note: In order to solve this question, one can get confused while constructing circles with different radius such that a new circle formed should be intersected by the previous circles. Also we must concentrate that the required tangents will be formed from the intersection points of the new circle formed.