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The question is to find the measure of arc PQ in Circle A. The point A is the center of the circle, and the chords PR and SQ intersect at the center. Arc PQ is (3y-10), while arc SR is (2y+20).

I know there's a theorem that states that when two chords intersect in the interior of the circle at the center, the measure of the angles are 1/2 the sum of the the two arcs.

I tried applying the theorem, but I doubt it's right because Y would equal a negative value:
1/2 * (3y-10 + 2y+20)
1/2 * (5y+10)
(2.5y+5)
-5 = 2.5y
y = -2 ?

Help please! It's much appreciated.

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Nikki

  1. The key point is that the two chords pass through the centre, making both of them diameters, and thus equal

    since the two central angles QAP andRAS are equal, their arcs are equal
    so
    3y-10 = 2y+20
    y = 30

    then arc PQ = 3y-10 = 80

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    Reiny

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