Question

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Answer 1

Step 1: Draw a circle and two non–parallel chords​
1) Draw a circle with the help of a bangle.​
2) Draw two non–parallel chords $AB$ and $CD.$
Step 2: Draw the center of the circle​
1) Draw the perpendicular bisector of $AB.$​
2) Draw the perpendicular bisector of $CD.$​
3) Two perpendicular bisectors $AB$ and $CD$ intersect at $O$ which is the center of the circle.

Step 3: Draw the tangents of the circle​
1) Take Point $P$ outside the circle.​
2) Join $PO$ and draw the perpendicular bisector of $PO$ such that it intersects $PO$ at point $M.$​
3) Taking $M$ as center and $MP$ as radius and draw a circle.​
4) Now two circles intersect at $R$ and $Q.$​
5) Join $PR$ and $PQ$ which are the required tangents of the circle.