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.3

Draw a circle of radius 3 cm.

Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its centre.

Draw tangents to the circle from these two points P and Q. Give the justification of the construction.

The tangent can be constructed on the given circle as follows:

Step 1. Taking any point O on the given plane as centre, draw a circle of 3 cm radius.

Step 2. Take one of its diameters, PQ, and extend it on both sides.

Locate two points on this diameter such that OR = OS = 7 cm.

Step 3. Bisect OR and OS. Let T and U be the mid-points of OR and OS respectively.

Step 4. Taking T and U as its centre and with TO and UO as radius, draw two circles.

These two circles will intersect the circle at point V, W, X, Y respectively.

Join RV, RW, SX, and SY. These are the required tangents.

Justification:

The construction can be justified by proving that RV, RW, SY, and SX are the tangents to the circle (whose centre is O and radius is 3 cm).

For this, join OV, OW, OX, and OY.

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

So, ∠RVO = 90⁰

=> OV ⊥ RV

Since OV is the radius of the circle, RV has to be a tangent of the circle.

Similarly, OW, OX, and OY are the tangents 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.