Lina Z.
asked • 01/04/20A thing I've been thinking about
Can the Secant-Secant Theorem ( If two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant) apply to two circles, with both secants originating from one point, and the secant A being in circle A, while secant B is in circle B, with circles A and B having different radii?
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1 Expert Answer
Mark H. answered • 01/04/20
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No, the theorem assumes one circle. You could apply a scaling factor to account for the difference in radius, but the overall problem seem a bit convoluted.
What is your top-level question/problem?
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Lina Z.
The question is "QR is tangent to both of the circles. Is it true or false that QS (external segment)⋅QT(whole segment)=QU (external)⋅QV (whole) because of the secant-secant product theorem?" Indeed QS⋅QT=QU⋅QV, because of QS⋅QT=QR^2=QU⋅QV, so should it be true or false?01/04/20