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Standard VII

Mathematics

Construction of Incircle of a Triangle

Construct a t...

Question

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

${86.5}^{o}$

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${76.5}^{o}$

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${66.5}^{o}$

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${56.5}^{o}$

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Solution

The correct option is B
${76.5}^{o}$

∠BAC is ${76.5}^{0}$ .

Step 1: Draw a line, AC, 5 cm long.
Step 2: Cut an arc AB= 5.5 Cm with A as the center.
Step 3: Cut an arc CB= 6.5cm with c as the center.
Step 4: Mark, B, the point of intersection of the two arcs.

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Similar questions

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

△ ABC

with

BC = 6.5 cm, AB = 5.5 cm

and

AC = 5 cm

. Find the radius of the incircle approximately.

Q. Construct a triangle

A B C

, in which

A B = 5.5 c m, A C = 6.5 c m

and

∠ B A C = 75^{\circ}

.
Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) At

A

, construct a line segment

A E

, sufficiently large, such that

∠ B A E = 75^{\circ}

, use protractor to measure

75^{\circ}

.
2) Draw a line segment which is sufficiently long using ruler.
3) With

A

as centre and radius

6.5 c m

, draw an arc cutting

A E

at C. Join

B C

. Hence,

A B C

is the required triangle.
4) Locate points

A

and

B

on it such that

A B = 5.5 c m

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.

Q. Construct a triangle

A B C

, in which

A B = 5.5 c m, A C = 6.5 c m

and

∠ B A C = 70^{\circ}

.
If the stpes of construction are given as below the answer the following question:

Which is the 2nd step of construction?
1) At

A

, construct a line segment

A E

, sufficiently large, such that

∠ B A C

70^{\circ}

, use protractor to measure

70^{\circ}

2) Draw a line segment which is sufficiently long using ruler.
3) With

A

as centre and radius

6.5 c m

, draw the line cutting

A E

at C, join

B C

, then

A B C

is the required triangle.
4) Locate points

A

and

B

on it such that

A B = 5.5 c m

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

The correct option is B 76.5o ∠BAC is 76.50. Step 1: Draw a line, AC, 5 cm long. Step 2: Cut an arc AB= 5.5 Cm with A as the center. Step 3: Cut an arc CB= 6.5cm with c as the center. Step 4: Mark, B, the point of intersection of the two arcs.

The correct option is B
${76.5}^{o}$

∠BAC is ${76.5}^{0}$ .

Step 1: Draw a line, AC, 5 cm long.
Step 2: Cut an arc AB= 5.5 Cm with A as the center.
Step 3: Cut an arc CB= 6.5cm with c as the center.
Step 4: Mark, B, the point of intersection of the two arcs.