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Circles touching two lines and each other: ratio of radii from the angle

This type of question, asked 2 times: CDS 2 2017, CDS 1 2020. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    58
    Two straight lines AB and AC include an angle. A circle is drawn in this angle which touches both these lines. One more circle is drawn which touches both these lines as well as the previous circle. If the area of the bigger circle is 9 times the area of the smaller circle, then what must be the angle A ?

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  2. Question 2

    CDS 1 2020

    73
    A circle of diameter 8 cm is placed in such a manner that it touches two perpendicular lines. Then another smaller circle is placed in the gap such that it touches the lines and the circle. What is the diameter of the smaller circle ?

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