ΔABC ~ ΔLBN . In ΔABC , AB = 5 . 1 cm , ∠ B = 40 ° , BC = 4 . 8 cm , AC LN = 4 7 . Construct ∆ ABC and ∆ LBN .

Steps of Construction: Draw ∆ ABC such that AB = 5 . 1 cm , ∠ B = 40 ° , BC = 4 . 8 cm . Divide segments BC into 4 equal points. Mark point N on ray BC such that length of BN is seven times of each part of segment BC . Draw a line parallel to side AC , through N . Name the point where the parallel line intersects ray AB as L . . Here, ∆ ABC ~ ∆ LBN

Construct ∆ PYQ such that, PY = 6 . 3 cm , YQ = 7 . 2 cm , PQ = 5 . 8 cm . If YZ YQ = 6 5 , then construct ∆ XYZ similar to ∆ PYQ .

Steps of construction: (i) Draw a line segment Y Q of 7 . 2 c m . Taking Y and Q as centre, draw arcs of radius 6 . 3 c m and 5 . 8 c m respectively. Let these arcs intersect each other at point P . △ P Y Q is the required triangle having the length of sides as 5 . 8 c m , 6 . 3 c m and 7 . 2 c m respectively. (ii) Draw any ray Y R making an acute angle with line Y Q on opposite side of vertex P . (iii) Locate 6 points Y 1 , Y 2 , Y 3 , Y 4 , Y 5 , Y 6 (as 6 is greater between 5 and 6 ) on Y R such that Y Y 1 = Y 1 Y 2 = Y 2 Y 3 = Y 3 Y 4 = Y 4 Y 5 = Y 5 Y 6 . (iv) Join Q Y 5 and draw a line through Y 6 parallel to Q Y 5 to intersect an extended line segment Y Q at point Z . (v) Draw a line through Z parallel to P Q intersecting the extended line segment Y P at X . △ X Y Z is required triangle. Hence, the required figure is as shown below:

E M B I B E

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4

Maharashtra Board Solutions for Chapter: Geometric Constructions, Exercise 3: Problem set 4

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Geometric Constructions, Exercise 3: Problem set 4

Attempt the practice questions on Chapter 4: Geometric Constructions, Exercise 3: Problem set 4 with hints and solutions to strengthen your understanding. Geometry Standard X solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Geometric Constructions, Exercise 3: Problem set 4 with Hints & Solutions

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>Q 1

If $∆ ABC ~ ∆ PQR$ and $\frac{AB}{PQ} = \frac{7}{5},$ then

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>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 $P .$

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>Q 3

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

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>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 $R .$

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>Q 5

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

MEDIUM

10th Maharashtra Board

IMPORTANT

Geometry Standard X>Chapter 4 - Geometric Constructions>Problem set 4>Q 6

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