Geometry · Textbook solutions

Geometric Constructions

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 27 questions

Construction of Similar Triangle

3 q

Solved Examples

Worked · 3
  1. Construction of Similar Triangle SolvedEx.1
    △ABC∼△PQR\triangle ABC \sim \triangle PQR, in △ABC\triangle ABC, AB = 5.4 cm, BC = 4.2 cm, AC = 6.0 cm. AB : PQ = 3 : 2. Construct △ABC\triangle ABC and △PQR\triangle PQR.
  2. Construction of Similar Triangle SolvedEx.2
    Construct any △ABC\triangle ABC. Construct △A′BC′\triangle A'BC' such that AB : A'B = 5 : 3 and △ABC∼△A′BC′\triangle ABC \sim \triangle A'BC'.
  3. Construction of Similar Triangle SolvedEx.3
    Construct △A′BC′\triangle A'BC' similar to △ABC\triangle ABC such that AB : A'B = 5 : 7.

Practice set 4.1

4 q
  1. Ex 4.1 Q.1
    △ABC∼△LMN\triangle ABC \sim \triangle LMN. In △ABC\triangle ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct △ABC\triangle ABC and △LMN\triangle LMN such that BCMN=54\dfrac{BC}{MN} = \dfrac{5}{4}.
  2. Ex 4.1 Q.2
    △PQR∼△LTR\triangle PQR \sim \triangle LTR. In △PQR\triangle PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct △PQR\triangle PQR and △LTR\triangle LTR, such that PQLT=34\dfrac{PQ}{LT} = \dfrac{3}{4}.
  3. Ex 4.1 Q.3
    △RST∼△XYZ\triangle RST \sim \triangle XYZ. In △RST\triangle RST, RS = 4.5 cm, ∠RST=40∘\angle RST = 40^\circ, ST = 5.7 cm. Construct △RST\triangle RST and △XYZ\triangle XYZ, such that RSXY=35\dfrac{RS}{XY} = \dfrac{3}{5}.
  4. Ex 4.1 Q.4
    △AMT∼△AHE\triangle AMT \sim \triangle AHE. In △AMT\triangle AMT, AM = 6.3 cm, ∠TAM=50∘\angle TAM = 50^\circ, AT = 5.6 cm. AMAH=75\dfrac{AM}{AH} = \dfrac{7}{5}. Construct △AHE\triangle AHE.

Construction of a tangent to a circle at a point on the circle

2 q

Solved Examples

Worked · 2
  1. Construction of a tangent to a circle at a point on the circle SolvedEx.1
    Draw a circle with centre C. Take any point P on the circle. Construct the tangent to the circle at point P, using the centre of the circle.
  2. Construction of a tangent to a circle at a point on the circle SolvedEx.2
    Construct a circle of any radius. Take any point C on it. Construct a tangent to the circle without using centre of the circle.

To construct tangents to a circle from a point outside the circle.

1 q

Solved Example

Worked · 1
  1. To construct tangents to a circle from a point outside the circle SolvedEx.1
    Construct a circle of any radius with centre O. Take any point P in the exterior of the circle. Construct tangents to the circle from point P.

Practice set 4.2

7 q
  1. Ex 4.2 Q.1
    Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
  2. Ex 4.2 Q.2
    Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.
  3. Ex 4.2 Q.3
    Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.
  4. Ex 4.2 Q.4
    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.
  5. Ex 4.2 Q.5
    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.
  6. Ex 4.2 Q.6
    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.
  7. Ex 4.2 Q.7
    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

10 q
  1. Select the correct alternative for each of the following questions.
    PS4 Q.1 (1)
    The number of tangents that can be drawn to a circle at a point on the circle is ............... .
    1. A.
      3
    2. B.
      2
    3. C.
      1
    4. D.
      0
  2. PS4 Q.1 (2)
    The maximun number of tangents that can be drawn to a circle from a point out side it is .............. .
    1. A.
      2
    2. B.
      1
    3. C.
      one and only one
    4. D.
      0
  3. PS4 Q.1 (3)
    If △ABC∼△PQR\triangle ABC \sim \triangle PQR and ABPQ=75\dfrac{AB}{PQ} = \dfrac{7}{5}, then ...............
    1. A.
      △ABC\triangle ABC is bigger.
    2. B.
      △PQR\triangle PQR is bigger.
    3. C.
      Both triangles will be equal.
    4. D.
      Can not be decided.
  4. PS4 Q.2
    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.
  5. PS4 Q.3
    Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.
  6. PS4 Q.4
    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.
  7. PS4 Q.5
    Draw a circle with centre P. Draw an arc AB of 100∘100^\circ measure. Draw tangents to the circle at point A and point B.
  8. PS4 Q.6
    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.
  9. PS4 Q.7
    △ABC∼△LBN\triangle ABC \sim \triangle LBN. In △ABC\triangle ABC, AB = 5.1 cm, ∠B=40∘\angle B = 40^\circ, BC = 4.8 cm, ACLN=47\dfrac{AC}{LN} = \dfrac{4}{7}. Construct △ABC\triangle ABC and △LBN\triangle LBN.
  10. PS4 Q.8
    Construct △PYQ\triangle PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If YZYQ=65\dfrac{YZ}{YQ} = \dfrac{6}{5}, then construct △XYZ\triangle XYZ similar to △PYQ\triangle PYQ.