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Chapter 4: Geometric Constructions TextBook Solution

Practice Set 4.1 | Q 1 | Page 96

Δ ABC ~ Δ LMN. In Δ ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. If MN = 4.8 cm, then construct Δ ABC and Δ LMN such that BC/MN = 5/4

Practice Set 4.1 | Q 2 | Page 96

∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `”PQ”/”LT” = 3/4`.

Practice Set 4.1 | Q 3 | Page 96

∆RST ~ ∆XYZ. In ∆RST, RS = 4.5 cm, ∠RST = 40°, ST = 5.7 cm Construct ∆RST and ∆XYZ, such that \[\frac{RS}{XY} = \frac{3}{5} .\]

Practice Set 4.1 | Q 4 | Page 96

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `”AM”/”AH” = 7/5`. Construct ∆AHE.

Practice Set 4.2 | Q 1 | Page 98

Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

Practice Set 4.2 | Q 2 | Page 98

Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.

Practice Set 4.2 | Q 3 | Page 98

Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Practice Set 4.2 | Q 4 | Page 98

Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your obeservation about the tangents.

Practice Set 4.2 | Q 5 | Page 99

Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.

Practice Set 4.2 | Q 6 | Page 99

Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

Practice Set 4.2 | Q 7 | Page 99

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

Problem Set 4 | Q 1.1 | Page 99

Select the correct alternative for the following question.

The number of tangents that can be drawn to a circle at a point on the circle is …………… .

Problem Set 4 | Q 1.2 | Page 99

Select the correct alternative for the following question.

The maximum number of tangents that can be drawn to a circle from a point out side it is ………….. .

one and only one

Problem Set 4 | Q 1.3 | Page 99

Select the correct alternative for the following question.

(3) If ∆ABC ~ ∆PQR and `(AB)/(PQ) = 7/5`, then ……………

∆ABC is bigger.

∆PQR is bigger.

Both triangles will be equal.

Can not be decided.

Problem Set 4 | Q 2 | Page 99

Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Problem Set 4 | Q 3 | Page 99

Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.

Problem S et 4 | Q 4 | Page 99

Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.

Problem Set 4 | Q 5 | Page 99

Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Problem Set 4 | Q 6 | Page 99

Draw a circle of radius 3.4 cm and centre E. Take a point F on the circle. Take another point A such that E-F-A and FA = 4.1 cm. Draw tangents to the circle from point A.

Problem Set 4 | Q 7 | Page 99

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1cm, ∠B = 40°, BC = 4.8 cm,\[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.

Problem Set 4 | Q 8 | Page 99

Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.

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