NCERT solution Class 10 constructions

NCERT Solutions

Class 10 Maths

Constructions

NCERT Questions

Ex.11.1 Q.1
Ex.11.1 Q.2
Ex.11.1 Q.3
Ex.11.1 Q.4
Ex.11.1 Q.5
Ex.11.1 Q.6
Ex.11.1 Q.7
Ex.11.2 Q.1
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5
Ex.11.2 Q.6
Ex.11.2 Q.7

Ex.11.2 Q.2

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length.

Also verify the measurement by actual calculation.

Give the justification of the construction.

Tangents on the given circle can be drawn as follows:

Step 1. Draw a circle of 4 cm radius with centre as O on the given plane.

Step 2. Draw a circle of 6 cm radius taking O as its centre.

Locate a point P on this circle and join OP.

Step 3. Bisect OP. Let M be the mid-point of PO.

Step 4. Taking M as its centre and MO as its radius, draw a circle.

Let it intersect the given circle at the points Q and R.

Step 5. Join PQ and PR. PQ and PR are the required tangents.

It can be observed that PQ and PR are of length 4.47 cm each.

In ∆PQO,

Since PQ is a tangent,

∠PQO = 90⁰

PO = 6 cm

QO = 4 cm

Applying Pythagoras theorem in ∆PQO, we obtain

PQ² + QO² = PQ²

=> PQ² + 4² = 6²

=> PQ² + 16 = 36

=> PQ² = 36 − 16

=> PQ² = 20

=> PQ = √20

=> PQ = 4.47 cm

Justification:

The construction can be justified by proving that PQ and PR are the tangents to the circle

(whose centre is O and radius is 4 cm). For this, let us join OQ and OR.

∠PQO is an angle in the semi-circle. We know that angle in a semi-circle is a right angle.

So, ∠PQO = 90⁰

=> OQ ⊥ PQ

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

Similarly, PR is a tangent of the circle.

Video solution:

Constructions Class 10 Maths NCERT Chapter 11 NCERT Solutions

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NCERT solutions of Constructions Class 10 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 10 Maths Constructions NCERT solutions.