Question

Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.

Answer 1

Steps of Construction:
Step 1: Draw a circle with any radius and mark any point A on it.
Step 2: Draw chord AB and an inscribed ∠BCA.
Step 3: With the centre C and any convenient radius draw an arc intersecting the sides of ∠ACB in points M and N.
Step 4: Using the same radius and centre A, draw an arc intersecting the chord AB at point O.
Step 5: Taking the radius equal to d(MN) and centre O, draw an arc intersecting the arc drawn in step 4. Suppose D be the point of intersection of these arcs. Draw line AD.

Here, line AD is the required tangent to the circle.