Question

Draw two circles whose distance between centres is $5.0cm$ and their radii are $1.5cm$ and $2.5cm$ respectively. Construct transverse common tangents to both the circles. Write their measures also. Write also steps of construction.

Answer 1

Steps of Construction:

1. Draw the two circles of radius 1.5 cm with center A and 2.5 cm with center B such that AB = 5 cm
2. Join AB. Draw a third circle with center B and radius 1.5 + 2.5 = 4cm (R1 + R2).
3. Bisect AB at X. (As done by the red line)
4. With center as X and radius AX, draw a semi-circle intersecting the third circle at R.
5. Join BR to cut the circle with center B and radius 2.5cm at Q.
6. Draw $AP||RB$
7. Join PQ

PQ is the required transverse common tangent

Measure of PQ = $\sqrt{A{B}^2-(R_1+R_2{)}^2}$

= $\sqrt{5^2-4^2}$

= $3cm$