CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 3:

Construct a triangle with sides , and and then another triangle whose sides are of the corresponding sides of the first triangle.

To Construct a Triangle of Sides

Answer:

To construct: To construct a triangle of sides 5 cm, 6 cm and 7 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.

Steps of construction:

(a) Draw a triangle ABC of sides , and .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate points and on BX such that .

(d) Join and draw a line through the point , draw a line parallel to intersecting at the point . ′

(e) Draw a line through C ‘parallel to the line CA to intersect BA at A’ .

Then, A ‘BC’ is the required triangle.

Justification:

[By construction]

[AA similarity]

[By Basic Proportionality Theorem]

But

Therefore,

Question 4:

Construct a tangent to a circle of radius from a point on the concentric circle of radius and measure its length. Also verify the measurement by actual calculation.

Answer:

Construct a Tangent to a Circle of Radius

To construct: To construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its lengths. Also, to verify the measurements by actual calculation.

Steps of Construction:

(a) Join PO and bisect it. Let be the mid-point of PO.

(b) Taking M as centre and MO as radius, draw a circle. Let it intersects the given circle at the point Q and R.

(c) Join .

Then PQ is the required tangent.

By measurement,

By actual calculation,

Justification: Join . Then is an angle in the semicircle and therefore,

Since OQ is a radius of the given circle, PQ has to be a tangent to the circle.