Question

Draw a circle of radius $5cm.$ Take a point $P$ on it. Without using the centre of the circle construct a tangent at the point $P$. [3 MARKS]

Answer 1

Construction: 2 Marks

Steps of construction: 1 Mark

In any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

Steps of construction :

1. Draw a circle of radius $5cm.$

2. Mark a point $P$ on it.

3. Draw any chord $PQ.$

4. Take a point $R$ on the major arc $QP.$

5. Join $PR$ and $RQ.$

6. Make $\angle QPT=\angle PRQ$ [$\because$ Angles in the alternate segments are equal]

7. Produce $TP$ to $T^{\prime },$ as shown in the figure.

8. $T^{\prime }PT$ is the required tangent at P.