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:220

Questions No:1

# Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.

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A Pair to tangents to the given circle can be constructed as follow.

Step 1:

Takking any point 0 of the given plane as centre, draw a circle of 6 cm radius. Locat point P, 10 cm away from O. Join OP.

Step 2

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

Step 3

Taking M as centre and MO as dadius, draw a circle.

Step 4

Let this circle intersect the previous circle at point Q and R.

Step 5

Join PQ and PR. PQ and PR are the required tangents. The lengths of tangents PQ and PR are 8 cm each.

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 6 cm ). For this, join OQ and OR.

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

∴ ∠PQO = 90° ⇒ 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.