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PD0083 · Problem 148

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Problem

A circle in the xyxy-plane has center (h,k)(h, k) and passes through (h+6,k8)(h + 6, k - 8). The point (h+t,k+2t)(h + t, k + 2t) also lies on the circle for exactly two values of tt. What is the product of these two values?
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