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36

Part of 1976 IMO Longlists

Problems(1)

Area of region enclosed by tangents of 3 concentric circles

Source:

1/30/2011
Three concentric circles with common center OO are cut by a common chord in successive points A,B,CA, B, C. Tangents drawn to the circles at the points A,B,CA, B, C enclose a triangular region. If the distance from point OO to the common chord is equal to pp, prove that the area of the region enclosed by the tangents is equal to AB⋅BC⋅CA2p\frac{AB \cdot BC \cdot CA}{2p}
geometrytrigonometrygeometry unsolved