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Math Help - Points on a circle

  1. #1
    Senior Member Mukilab's Avatar
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    Points on a circle

    In the diagram, take O as the centre of the circle.

    P,q,R and S are points on the circle

    Angle ROP=110

    Calculate the angle RSP

    I did 360-110
    then 360-55
    Then 2*(305-250)=110

    rsp=110
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  2. #2
    MHF Contributor Unknown008's Avatar
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    The correct way to do it is to make use of angle PQR.

    From the properties of angles within a circle, we know that angle 2PQR = angle ROP

    Therefore, angle PQR = 110/2 = 55

    Now, from quadrilaterals inscribed within a circle, the sum of two opposite angles = 180 degrees.

    Therefore, 180 - 55 = RSP

    And RSP = 125 degrees
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  3. #3
    Senior Member Mukilab's Avatar
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    Interesting, do you have a place where I can shift through all of these laws? I'm studying for an exam and I have nothing but general knowledge to draw from, not knowing half of the requirements.
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  4. #4
    Senior Member nikhil's Avatar
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    Lightbulb easiest and correct method

    its very easy NO NEED TO CALCULATE ANGLE PQR
    angle PSR=(1/2)(angle POR in the major segment)
    angle POR in the major segment =360-110=250
    therfor
    angle PSR=(1/2)*250=125
    this is the easiest and shortest method
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  5. #5
    Senior Member Mukilab's Avatar
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    Thanks but where do you get these methods? Point me towards a website, book, anything please
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