web analytics

Slide9.JPG

Slide10.JPG
Slide11.JPG Slide12.JPG

-v-

Ex 11.2, 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.

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

  1. Taking any point O on the given plane as centre, draw a circle of 3 cm radius.
  2. Extend diameter of circle to a distance of 7 cm from centre on both sides.
  3. Let these points be P and Q. Where OP = OQ = 7 cm
  4. Bisect OR and OS. Let M and N be the mid-points of OP and OQ respectively.
  5. .Taking M as centre and MO as  radius, draw a circle. Do the same for point N. Let it intersect at points A, B and C, D respectively
  6. Join PA, PB, PC and PD

Thus, PA, PB, QC, QD are the required tangents

Justification:

We need to prove that PA, PB, QC, QD are the tangents to the circle.

Join OA and OB.

∠PAO is an angle in the semi-circle of the blue circle
And we know that angle in a
semi-circle is a right angle.

∴ ∠PAO = 90°

⇒ OA ⊥ PA

Since OA is the radius of the circle,

PA has to be a tangent of the circle.

Similarly, PB is a tangent of the circle.

Similarly, we can prove QC and QD are tangents

-ev-

  1. Chapter 11 Class 10 Constructions
  2. Concept wise
Ask Download

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail