Question

Take a point O on the plane of the paper. With O as center draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.

Answer 1

Hint: First of all draw a circle with center O and radius 3 cm. Now draw a radius OP and then draw a line perpendicular to OP at P. This line is our required tangent. Here we required some equipment like a protector, compass to construct the tangent.

Complete step-by-step solution -
In this question, we have to take a point O on the plane of the paper. With O as center and radius 3 cm, we have to draw a circle. Now at any point P on the circle, we have to draw a tangent at P.
1. First of all, take a point on a plane and mark it O.

2. Now, with O as center and radius = 3 cm. Draw a circle with the help of the compass.

3. Now, mark a point P on the circumference of the circle and join O to P.

4. Here OP is the radius of the circle of 3 cm. Now we have to draw a tangent at P. We know that the tangent is always perpendicular to the radius of the circle at the point of tangency. So, basically, we have to draw a line perpendicular to OP at P.

5. Now extent P outside the circle to point E.

6. Now with P as the center and any radius say 2 cm, cut an arc on the line OP and name it A.

7. Now, again with P as the center and with the same radius, draw another arc on line PE and name it ‘B’.

8. Now with A as a center and any radius greater AP, draw an arc on the left side of the line OE.

9. Now, with B as center and with the same radius, draw an arc cutting the previous arc and name the point Q.

10. Now, join point Q to point P and extend it. Here PQ is our required tangent.

Hence, we have drawn a tangent at point P of the circle of radius 3 cm.

Note: In this question, students can verify their construction by measuring the angle OP as by protractor if it is the right angle or not. Also, students must remember that tangent is always perpendicular to the radius at the point of tangency. Some students make this mistake of drawing a perpendicular bisector but we need to draw the perpendicular at point P.