Question

Draw a circle of radius 3.5 cm. Take two points A and B on one of its extended diameter, each at a distance of 5 cm from its center. Draw tangents to the circle from each of these points A and B.

Answer 1

Steps of Construction
Step 1: Draw a circle with center O and radius 3.5 cm.
Step 2: Extends its diameter on both sides and mark two points A and B on it such that OA =OB = 5 cm.
Step 3: Draw the perpendicular bisectors of OA and OB. Let C and D be the mid-points of OA and OB, respectively.
Step 4: Draw a circle with C as center and radius OC (or AC), to intersect the circle with center O, at the points P and Q.
Step 5: Draw another circle with D as center and radius OD (or BD), to intersect the circle with center O at the points R and S.
Step 6: Join AP and AQ, Also, join BR and BS.

Here, AP and AQ are the tangents to the circle from A, Also, BR and BS are the tangents to the circle from B.