Exercise 1
Draw a regular hexagon of side 4 cm and construct its incircle.
Solution: Steps to construct: Step 1: Draw a regular hexagon of sides 4cm. Step 2: Draw the angle bisector of A and B. which intersects each other at point O. Step 3: Draw OL perpendicular to AB....
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
Solution: Steps to construct: Step 1: Draw a line segment AB = 4cm. Step 2: At points A and B draw rays making on angle of 120o each and cut off AF = BC = 4cm. Step 3: At point C and F draw rays...
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 is drawn a perpendicular to AB and CA respectively. What is the relation between OR and OQ? (iii) What is the relation between ∠ACO and ∠BCO?
Solution: (i) The point O where the angle bisectors meet is called the incenter of the triangle. (ii) The perpendicular drawn from point O to AB and CA are equal. i.e., OR and OQ. (iii) ∠ACO = ∠BCO....
(i) Conduct a triangle ABC with BC = 6.4 cm, CA = 5.8 cm and ∠ ABC = 60°. Draw its incircle. Measure and record the radius of the incircle. (ii) Construct a ∆ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle. (2014)
Solution: Steps to construct: Step 1: Draw a line segment BC = 6.4cm. Step 2: Construct an angle of 60o at point B. Step 3: With C as center and radius CA = 5.8cm, draw an arc cutting BD at A. Step...
Using a ruler and compasses only: (i) Construe a triangle ABC with the following data: Base AB = 6 cm, AC = 5.2 cm and ∠CAB = 60°. (ii) In the same diagram, draw a circle which passes through the points A, B and C. and mark its centre O.
Solution: Steps to construct: Step 1: Draw a line segment AB = 6cm. Step 2: At point A, draw a ray making an angle of 60o. Step 3: With B as the center and radius 5.2cm, draw an arc which intersects...
Construct a triangle with sides 3 cm, 4 cm and 5 cm. Draw its circumcircle and measure its radius.
Solution: Steps to construct: Step 1: Draw a line segment BC = 4cm. Step 2: With Center as B and radius 3cm, with center as C and radius 5cm draw two arcs which intersect each other at point A. Step...
Using a ruler and a pair of compasses only, construct: (i) A triangle ABC given AB = 4 cm, BC = 6 cm and ∠ABC = 90°. (ii) A circle which passes through the points A, B and C and mark its centre as O. (2008)
Solution: Steps to construct: Step 1: Draw a line segment AB = 4cm. Step 2: At point B, draw a ray BX making an angle of 90o and cut off BC = 6cm. Step 3: Join AC. Step 4: Draw the perpendicular...
Draw an equilateral triangle of side 4 cm. Draw its circumcircle.
Solution: Steps to construct: Step 1: Draw a line segment BC = 4cm. Step 2: With centers B and C, draw two arcs of radius 4cm which intersects each other at point A. Step 3: Join AB and AC. Step 4:...
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Solution: Steps to construct: Step 1: Draw a line segment AB = 8cm. Step 2: With center as A and radius 4cm, with center as B and radius 3cm, draw circles. Step 3: Draw the third circle AB as...
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Solution: Steps to construct: Step 1: Consider a point O on a line, with center O, and radius 3cm, draw a circle. Step 2: Extend its diameters on both sides and cut off OP = OQ = 7cm. Step 3: Mark...
Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent
Solution: Steps to construct: Step 1: Draw a line segment AB = 6cm. Step 2: Draw its perpendicular bisector bisecting it at point O. Step 3: With center O and radius OB, draw a circle. Step 4:...
Use a ruler and compass only in this question. (i) Draw a circle, centre O and radius 4 cm. (ii) Mark a point P such that OP = 7 cm. Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.
Solution: Steps to construct: Step 1: Draw a circle with center O and radius 4cm and mark that point as A. Step 2: Take a point P such that OP = 7cm. Step 3: Bisect OB at M. Step 4: With center M...