Steps to construct the required figure:
Step 1: Draw a line segment AB of 8 cm.
Step 2. Taking A as centre , draw a circle of radius 4 cm and taking B as centre, draw a circle of radius 3 cm.
Step 3. With M as centre which is the center of line AB, draw a circle of radius MA or MB, intersecting circle with centre B at R and S, circle with center as A at P and Q.
Step 4. Join AR,AS, BP and BQ and hence we got the required tangents.
On joining BP, we get \(\angle \) BPA=90° ; [\(\therefore \) BPA is the angle in the semi-circle]
Therefore, AP \(\perp \) BP
So,AP is the tangent to the circle because BP is the radius of the given circle.
Similarly, AR,BQ and AS are the tangents.