Construction of Incircle of a Triangle

Q.

Construct a triangle ABC with BC = 6.5 cm, AB = 5.5 cm and AC = 5 cm. ∠BAC is (use protractor)

1. ${76.5}^o$

2. ${66.5}^o$

3. ${56.5}^o$

4. ${86.5}^o$

Q. Locate the incentre of the right angled triangle shown below.

Q.

Construct an isosceles triangle in which the lengths of each of its equal sides

is 6.5 cm and the angle between them is 110°.

Q. Choose the lengths of the sides yourself and draw one equilateral, one isosceles and one scalene triangle.

Q.

The steps of construction of an isosceles triangle PQR with angle PQR as 110^o are as follows:

(i) Draw the base QR.

(ii) Join P to R to obtain the required triangle PQR.

(iii) At point Q, draw a ray QX making an angle 110° with QR.

(iv) Taking Q as centre, draw an arc of radius equal to PQ. It intersects QX at the point P.

The correct order of steps is

1. (i), (iii), (iv), (ii)

2. (i), (iii), (ii), (iv)

3. (i), (ii), (iii), (iv)

4. (i), (iv), (ii), (iii)

Q. Construct ∆EFG from the given measures. l(FG) = 5 cm, m$\angle$EFG = 90^°, l(EG) = 7 cm.

Q.

Triangle ABC is constructed with BC = 5.5 cm, AB = 5.5 cm and AC = 5 cm. Two angular bisectors are drawn of angle A and C intersected at point O. Drop a perpendicular OD on any of the sides of the triangle. The length of OD is:

1. 1.53 cm

2. 1.9 cm

3. 2.2 cm

4. 1.3 cm

Q.

Construct a triangle ABC with BC = 6.5 cm, AB = 5.5 cm and AC = 5 cm. Construct the incircle of the triangle. The radius of the incircle is

1. 1.3 cm

2. 1.6 cm

3. 1.9 cm

4. 2.2 cm

Q. (1) Draw ∆ABC, such that l (AB) = l (AC) = 4.2 cm and l (BC) = 6 cm.

Q. (2) Draw ∆XYZ, such that l (XY) = 5 cm, l (YZ) = 5.6 cm and l (XZ) = 4.2 cm.

Q. Take any three non-collinear points A, B, C and draw ∆ABC. Through each vertex of the triangle, draw a line parallel to the opposite side.

Q.

Construct an isosceles right-angled triangle ABC, where, m∠ACB = 90° and AC = 6 cm.

Q.

Triangle ABC is constructed with BC = 5.5 cm, AB = 5.5 cm and AC = 5 cm. Draw two angular bisectors of angle A and C. These two bisectors will intersect at a point.

1. True

2. False

Q. Construct a ∆PQR in which QR = 6 cm, PQ = 4.4 cm and PR = 5.3 cm. Draw the bisector of ∠P.

Q.

Triangle ABC is constructed with BC = 5.5 cm, AB = 5.5 cm and AC = 5 cm. Two angular bisectors are drawn of angle A and C intersected at point O. Drop a perpendicular OD on any of the sides of the triangle. The length of OD is ____.

1. 1.3 cm

2. 1.53 cm

3. 1.9 cm

4. 2.2 cm

Q. Take any three non-collinear points A, B, C and draw ∆ABC. Through each vertex of the triangle, draw a line parallel to the opposite side.

Q. Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 80°. Measure AB. Is (AB)² = (AC)² + (BC)²? If not, which one of the following is true:
(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

Q. Draw triangles according to the following measures.

(1) In ∆PQR, l (PQ) = 4.9 cm, l (QR) = 5.3 cm, m∠Q = 50°
(2) In ∆LMN, l (LM) = 4 cm, l (MN) = 5 cm, m∠M = 70°
(3) In ∆DEF, l (DE) = l (DF) = 6 cm, m∠D = 40°
(4) In ∆BCD, m∠B = 110°, l (BC) = l (BD) = 6.2 cm

Q. Draw ∆ ABC in which AB = 5.5 cm, BC = 6 cm and CA = 7 cm. Also, draw perpendicular bisector of side BC.

Q. Draw a triangle ABC with AB = 6 cm, BC = 7 cm and CA = 8 cm. Using ruler and compass alone, draw (i) the bisector AD of ∠A and (ii) perpendicular AL from A on BC. Measure LAD.