Ved Prakash Sharma
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Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

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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:4

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2 Answers

  1. The tangents can be constructed in the following manner:
    Step 1
    Draw a circle of radius 5 cm and with centre as O.
    Step 2
    Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.
    Step 3
    Draw a radius OB, making an angle of 120° (180° – 60°) with OA.
    Step 4
    Draw a perpendicular to OB at point B. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of 60°.
    Justification
    The construction can be justified by proving that ∠APB = 60°
    By our construction
    ∠OAP = 90° ∠OBP = 90° and ∠AOB = 120°
    We know that the sum of all interior angles of a quadrilateral = 360°
    ∠OAP + ∠AOB + ∠OBP + ∠ABP = 360° ⇒ 90° + 120° + 90° + ∠APB = 360°
    ∠APB = 60°
    This justifies the construction.

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  2. 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/

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