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Thread: Radians: Points A, B, C and D divide circumference of circle in the ratio 1:2:3:4...

  1. #1
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    Radians: Points A, B, C and D divide circumference of circle in the ratio 1:2:3:4...

    Question: Points A, B, C and D divide the circumference of a circle in the ratio 1:2:3:4. Find the angles of the cyclic quadrilateral ABCD in radians.
    The answers are 3pi/10, pi/2, 7pi/10 and pi/2.

    But I don't really understand because what I calculated are 36, 72, 108, 144 degrees respectively. [using 360/(1+2+3+4) and multiply the ratio]. How can I get the above answer?? Thanks

  2. #2
    Elite Member
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    You have done well to use Central Angles to solve the first part.

    Now, draw the rectangle and switch your thinking to Inscribed Angles.

    Hint: Each Inscribed Angle contains two of your circumference pieces.

    Let's see what you get!
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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