Question

Two different points P and Q are given on one side of line AB. Draw a circle passing through the points P and Q touching the line AB at point R.

Answer 1

Hint: First we will plot the point P. Now we will mark the point Q such that PQ = 6cm. Now let us take point C such that PC = 3cm. Now with point C as the center draw a circle such that it passes through points P and Q. Now we have a circle, which passes through points P and Q. Now let R be any point on the circle. Now draw a line passing through R such that it is tangent to the circle. Name this line segment AB.

Complete step-by-step solution:
Now first let us start by plotting point P in the paper.

Now from this point P, we will mark Point Q such that PQ is 6cm. Now join the points P and Q such that PQ = 6cm.

Now mark point C such that PC = 3cm.
Now note that PC = 3cm and PQ = 6cm hence we have QC = 3cm.
Hence c is equidistant from points P and Q. Let us draw a circle with center C and radius 3cm. Hence we will get the point P and Q lie on the circle as CP and CQ are also the radii of the circle.

Now let R be any point on the circle let us mark the point on the circle and draw a tangent through R. Hence we have.

Now mark A and B on the tangent so that we get line segment AB.

Hence we get the required diagram.

Note: Now here first note that we are given that the circle touches the line AB at point R. Whenever we have a line touching the circle at a point it is always the tangent of the circle. Now note that we can also start the following question by first drawing the line AB. Then first draw a circle such that the circle is tangent to line AB. Then mark point P and Q accordingly. It is important to first have a vision of what we are drawing hence first start withdrawing a rough figure.