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.