Asked in: June 2026 board paper (set among the Circle questions that year)Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at point P and Q. Write your observation about the tangents.

Answer: The chord PQ is a diameter, and the tangents at P and Q are parallel to each other.

Steps of construction:

1. Draw a circle with centre O and radius 3.3 cm.
2. Take a point P on the circle. With P as centre and radius 6.6 cm, draw an arc cutting the circle at Q. Draw chord PQ; it passes through O.
3. At P draw line l perpendicular to seg OP, and at Q draw line m perpendicular to seg OQ.
4. Lines l and m are the required tangents.

[Figure: circle with centre O, radius 3.3 cm; diameter PQ = 6.6 cm; tangent l at P and tangent m at Q, both perpendicular to PQ.]

Observation: 6.6 cm = 2 × 3.3 cm, so chord PQ is a diameter. Both tangents are perpendicular to the same line PQ, so they are parallel (l || m) and never meet.