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Let ABCD be a square of side of unit length. Let a circle C1 centred at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is , where α,β are integers, then α + β  is equal to ________.
    Correct answer is '1'. Can you explain this answer?
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    Let ABCD be a square of side of unit length. Let a circle C1 centred a...

    Here, AO + OD = 1 or (√2 + 1) r = 1

    Equation of circle: (x - r)2 + (y - r)2 = r2
    Equation of CE:
    y - 1 = m (x - 1)
    mx - y + 1 - m = 0
    It is tangent to circle

    Put r = √2 - 1
    On solving, m = 2 - √3, 2 + √3
    Taking greater slope of CE as:
    2 + √3
    y - 1 = (2 + √3) (x - 1)
    Put y = 0
    -1 = (2 + √3) (x - 1)

    x - 1 = √3 - 1
    EB = 1 - x = 1 - (√3 - 1)
    EB = 2 - √3
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    Let ABCD be a square of side of unit length. Let a circle C1 centred at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is , where α,β are integers, thenα +β is equal to ________.Correct answer is '1'. Can you explain this answer?
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    Let ABCD be a square of side of unit length. Let a circle C1 centred at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is , where α,β are integers, thenα +β is equal to ________.Correct answer is '1'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let ABCD be a square of side of unit length. Let a circle C1 centred at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is , where α,β are integers, thenα +β is equal to ________.Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ABCD be a square of side of unit length. Let a circle C1 centred at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is , where α,β are integers, thenα +β is equal to ________.Correct answer is '1'. Can you explain this answer?.
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