Question

Draw a circle of radius 3 cm. Take a point at a distance of 5.5 cm from the center of the circle. From point \[P\], draw two tangents on the circle.

Answer 1

Hint: In this problem, first we need to draw a circle of radius 3 cm having a center at point \[O\]. Now, take a point \[P\] at a distance of 5.5 cm from the center of the circle. Draw a line joining the point \[O\] and \[P\]. Now draw a perpendicular bisector of the line \[OP\] that cuts \[OP\] at \[M\]. From point \[M\] draw a circle of radius \[OM\] which cuts the circle at points \[A\] and \[B\]. Next draw the line joining the points \[AP\] and \[BP\].

Complete step-by-step answer:
The steps for the construction of the tangents on the circle are as follows:
(a) Consider a point \[O\] as a center and draw a circle of radius 3 cm.
(b) Take a point \[P\] at a distance of 5.5 cm from the center of the circle.
(c) Draw a line joining the point \[O\] and point \[P\].
(d) Draw a perpendicular bisector the line \[OP\] that cuts \[OP\] at \[M\].
(e) From point \[M\] draw a circle of radius \[OM\] which cuts the circle of radius 3 cm at points \[A\] and \[B\].
(f) Draw the line joining the points \[AP\] and\[BP\], which represents the tangents on the circle as shown below.

Note: Take the perpendicular bisector of the line joining the points \[O\] and \[P\]. Point \[A\] and point \[B\] are the points of tangent on the circle.