ICSE Class 10th Mathematics Chapter 19 - Constructions Important Questions with Answers

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent. 

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.

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

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.  

Using ruler and compasses only,

1. Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ?ABC = 45°.
2. Inscribe a circle in the ?ABC constructed in (i) above. Measure its radius.

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,

1. Construct a triangle ABC with the following data :
   Base AB = 6 cm, BC = 6.2 cm and ?CAB = 60°.
2. In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
3. Draw a perpendicular from O to AB which meets AB in D.
4. Prove that : AD = BD.

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

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.

1. What do you call the point O?
2. What is the relation between the distances OA, OB and OC?
3. Does the perpendicular bisector of BC pass through O?