Question

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

Answer 1

Steps of Construction:
Step I: A line segment AB of 8 cm is drawn.
Step II: With A as center and radius equal to 4 cm, a circle is drawn which cut the line at point O.
Step III: With B as a center and radius equal to 3 cm, a circle is drawn.
Step IV: With O as a center and OA as a radius, a circle is drawn which intersect the previous two circles at P, Q, and R, S.
Step V: AP, AQ, BR, and BS are joined.
Thus, AP, AQ, BR, and BS are the required tangents.
Justification:
$\angle BPA={90}^{\circ }$ (Angle in the semi-circle)
$\therefore AP\perp PB$
Therefore, BP is the radius of the circle then AP has to be a tangent of the circle.
Similarly, AQ, BR, and BS are tangents of the circle.