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Circles centred at the vertices of a triangle touching each other: sum of radii = half the perimeter

This type of question, asked 2 times: CDS 1 2021, CDS 2 2021. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2021

    85
    The sides of a triangle ABCABC are 4 cm, 6 cm and 8 cm. With the vertices of the triangle as centres, three circles are drawn each touching the other two externally. What is the sum of the radii of the three circles?

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  2. Question 2 (case study, 3 parts)

    CDS 2 2021

    Consider the following for the next three (03) items that follow : ABCABC is a triangle with sides AB=6AB = 6 cm, BC=10BC = 10 cm and CA=8CA = 8 cm. With vertices AA, BB and CC as centres, three circles are drawn each touching the other two externally.
    81
    What is the sum of the radii of the circles ?

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    82
    What is the length of the altitude of the triangle drawn from vertex AA on BCBC ?

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    83
    If PP, QQ and RR are the areas of sectors at AA, BB and CC within the triangle respectively, then which of the following is/are correct ? 1. P=πP = \pi cm2^2 2. 9Q+4R=36π9Q + 4R = 36\pi cm2^2 Select the correct answer using the code given below :

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