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    Escribed Circle of Triangle - Practice Questions & MCQ

    Updated on Sep 18, 2023 18:34 AM

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    • 3 Questions around this concept.

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    QuestionEASY

    In a triangle with sides a,b,c,r_{1}> r_{2}> r_{3}  ( which are the ex-­radii) then:

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    Concepts Covered - 1

    Escribed Circle of Triangle

    Escribed Circle of Triangle

    The circle which touches the side BC and two sides AB and AC produced of triangle ABC is called the escribed circle opposite to the angle A. Its radius is denoted by r1. Similarly, r2 and r3 denote the radii of the escribed circles opposite to the angles B and C respectively. 

    Formulae for $r_1, r_2$ and $r_3$
    1. $r_1=\frac{\Delta}{s-a}, r_2=\frac{\Delta}{s-b}, r_3=\frac{\Delta}{s-c}$
    2. $r_1=s \tan \frac{A}{2}, r_2=s \tan \frac{B}{2}, r_3=s \tan \frac{C}{2}$
    3. $r_1=4 R \sin \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}$
    $r_2=4 R \cos \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}$
    $r_3=4 R \cos \frac{A}{2} \cos \frac{B}{2} \sin \frac{C}{2}$

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    Escribed Circle of Triangle

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    Escribed Circle of Triangle Current Topic

    Measuring Angles
    Trigonometric Ratios
    Trigonometric Identities
    Sign of Trigonometric Functions
    Graphs of General Trigonometric Functions
    Trigonometric Ratios of Allied Angles
    Trigonometric Ratios of Compound Angles
    Sum-to-Product and Product-to-Sum Formulas
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    Double Angle Formulas

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    Reference Books

    Escribed Circle of Triangle

    Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

    Page No. : 5.29

    Line : 45

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