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Right triangle in a circle of radius 10 with altitude 8 to the hypotenuse: area or product of the legs

This type of question, asked 2 times: CDS 2 2021, CDS 2 2022. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2021

    61
    The radius of circum-circle of a right-angled triangle is 10 cm and the altitude drawn to the hypotenuse is 8 cm. What is the area of the triangle ?

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  2. Question 2

    CDS 2 2022

    87
    A right-angled triangle ABC is inscribed in a circle of radius 10 cm. The altitude drawn to the hypotenuse AC is of length 8 cm. If AB = x cm and BC = y cm, then what is the value of xy ?

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