NCERT Solutions for Class 10 Maths Chapter 11

Important NCERT Questions

Constructions

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 11.2

Page No:221

Questions No:3

# Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its Centre. Draw tangents to the circle from these two points P and Q.

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The tangent can be constructed on the given circle as follow.

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 extent it on both sides. Locate two points on this diameter surch 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 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.

∴ ∠RVO = 90° ⇒ 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.