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Math Help - circle problems need help

  1. #1
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    circle problems need help

    in the accompanying diagram of circle o, ABD and AEC are secants chord BE and CD intersect at F tangents Gh intersect at F tangents Gh intersect circle o at C, mBD = 100, mDE = 70 and mEC = 80


    Find

    mBAC
    mBDC
    mCFE
    mGCE
    mAEB

    also this problem



    if PR = 10 Pq = 6 and PS = 5 find PT

    if PR = 12 Pq = 3 and PS = 2 find PT

    and this one

    in the accompanying diagram of circle o mAB = 64 and mAEB = 52



    what is the measure of CD
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  2. #2
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    In mBD = 100, what is m and what is 100?
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  3. #3
    Member rtblue's Avatar
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    For the first problem, using the fact that the angle formed by two secants is equal to the measure of the major arc minus the minor arc, all divided by two. But before we do anything there, determine the measure of arc BC:

    BC=360-(100+80+70)
    BC=110

    Therefore angle BAC = \frac{\110-70}{2}
    BAC=20

    since angle BDC is formed by 2 chords, it is half the measure of the arc formed by those 2 chords: BDC=\frac{\110}{2}
    BDC = 55

    For CFE you will take the average of 80 and a 100, which is 90.

    GCE will be half of its intercepted arc, which is 80, therefore GCE will be 40.

    AEB is the supplement of BEC, so AEB will be 180 - BEC. Since BEC is just half of 110 which is 55, AEB =180-55=125
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