Exercise 19A

### Construct a circle, inscribing an equilateral triangle with side 5.6 cm.

Steps for Construction: i) Draw a line segment BC = 5.6 cm ii) With centres B and C, draw two arcs of 5.6 cm radius each which intersect each other at A. iii) And, join AB and AC. iv) Draw angle...

### Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.

Steps for construction: i) Draw a line segment BC = 6 cm ii) Draw two arcs of radius 6 cm with centres B and C, which intersect each other at A. iii) Then, join AC and AB. iv) Draw perpendicular...

### i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm. ii) Find its incentre and mark it I.iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.

Steps for construction: i) Draw a line segment BC = 6 cm. ii) Draw an arc with centre B and radius 8 cm. iii) Draw another arc with centre C and radius 5 cm which intersects the first arc at A. iv)...

### The bisectors of angles A and B of a scalene triangle ABC meet at O. iii) What is the relation between angle ACO and angle BCO?

iii) OC is the bisector of angle C Thus, ∠ACO = ∠BCO

### 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 perpendiculars to AB and CA respectively. What is the relation between OR and OQ?

i) O is called the incentre of the incircle of ΔABC. ii) OR and OQ are the radii of the incircle and OR = OQ.

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

iii) Yes, the perpendicular bisector of BC will pass through O.

### Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O. (i) What do you call the point O? (ii) What is the relation between the distances OA, OB and OC?

i) O is called the circumcentre of circumcircle of ΔABC. ii) OA, OB and OC are the radii of the circumcircle.

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

Steps for Construction: i) Draw a line segment BC = 4 cm. ii) At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm. iii) Draw another perpendicular line EY from E. iv) From C, draw a...

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

Steps for construction: i) Draw a line segment AB = 6 cm ii) Draw a ray at A, making an angle of 60o with BC. iii) With B as centre and radius = 6.2 cm draw an arc which intersects AX ray at C. iv)...

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

Steps for Construction: i) Draw a line segment BC = 5 cm ii) With centres as B and C, draw two arcs of radius 5 cm each which intersect each other at A. iii) Then, join AB and AC. iv) Draw angle...

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

Steps for construction: A. Construction of triangle: a) Draw a line segment BC = 7 cm b) At B, draw a ray BX making an angle of 45o and cut off BE = AB – AC = 1 cm c) Join EC and draw the...

### 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.

Steps for construction: i) Draw a line segment BC = 4.5 cm ii) With centres B and C, draw two arcs of radius 4.5 cm which intersect each other at A. iii) And join AC and AB. iv) Draw the...

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

Steps for Construction: i)  draw a circle with centre O, with radius BC = 4.5 cm ii) Draw arcs making an angle of 180º – 60º = 120º at O such that ∠AOB = 120º iii) At A and B, draw two rays making...

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

Steps for construction: i)  draw a circle with centre O,with radius BC = 5 cm ii) Draw arcs making an angle of 180º – 45º = 135º at O such that ∠AOB = 135º iii) At A and B, draw two rays making an...