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:7

# Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Share

Get Hindi Medium and English Medium NCERT Solution for Class 10 Maths to download.

Please follow the link to visit website for first and second term exams solutions.

https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-11/

The required tangents can be constructed on the given circle as follows.

Step 1

Draw a circle with the help of a bangle.

Step 2

Take a point P outside this circle and take two chords QR and ST.

Step 3

Draw perpendicular bisectors of these chords. Let them intersect each other at point O.

Step 4

Join PO and bisect it. Let U be the mid-point of OP. Taking U as centre, draw a circle at V and W. Join PV and PW.

PV and PW are the required tangents.

Justification

The construction can be justified by proving that PV and PW are the tangents to the circle. For this, first of all, it has to proved that O is the centre of the circle. Let us join OV and OW.

We know that perpendicular bisector of a chord passes through the centre. Therefore, the perpendicular bisector of chords QR and ST pass through the centre. It is clear that the intersection point of these perpendicular bisectors is the centre of the circle. ∠PVO is an angle in the semi-circle. We know that an angle in the semi- circle is a right angle.

∴ ∠PVO = 90°

⇒ OV ⊥ PV

Since OV is the radius of the circle, PV has to be a tangent of the circle. Similarly, PW is a tangent of the circle.