Question

Draw a circle with centre P and radius 3 cm. Draw a chord MN of length 4 cm. Draw tangents to the circle through points M and N which intersect in point Q. Measure the length of seg PQ.

Answer 1

Rough diagram:

Steps of construction:

1. Draw a circle of 3 cm radius, with centre P.
2. Draw a chord MN of length 4 cm.
3. Draw a ray from centre P passing through point N on the circle.
4. Similarly, draw a ray from centre P passing through point M on the circle.
5. Draw line C ⊥ ray PM at point M.
6. Draw line d ⊥ ray PN at point N.
7. Extend tangents c and d to obtain intersecting point Q.
8. Draw a line joining P and Q and measure length PQ = 4 cm.

Construction: