Constructions (Circles) Mathematics - Constructions (Circles)

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O. 
Does the perpendicular bisector of BC pass through O? 

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What is the relation between the distances OA, OB and OC?

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What do you call the point O?

Draw a circle circumscribing a regular hexagon with side 5 cm.

The bisectors of angles A and B of a scalene triangle ABC meet at O.
(i) What is the point O called?
(ii) OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
(iii) What is the relation between angle ACO and angle BCO?

Using ruler and compasses only construct a triangle ABC in which BC = 4cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.

Using ruler and compasses only,
(i) Construct a triangle ABC with the following data:
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°
(ii) In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
(iii) draw a perpendicular from O to AB which meets AB in D.
(iv) Prove that AD = BD

Using ruler and compasses only,
(i) Construct triangle ABC, having given BC = 7cm, AB – AC = 1cm and ∠ABC = 45°.
(ii) Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :
1) A circle of radius 2.5 cm, passing through A and C.
2) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.

Using ruler and compasses only, draw an equilateral triangle of side 5 cm, draw its inscribed circle. Measure the radius of the circle.

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.

Draw a circle of radius 4.5 cm. draw two tangents to this circle so that the angle between the tangents is 60°.

Draw a circle of radius 5 cm. draw two tangents to this circle so that the angle between the tangents is 45°

Draw a circle of diameter 9 cm. mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this exterior point. Measure the length of each tangent