Perimeter Check

perimeter check

Two lines that intersect at A are tangent to a circle at B and C. AB and AC are both 10. If a third tangent (green) touches the circle somewhere between B and C, what is the perimeter of the triangle formed by the three lines?

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Two tangents drawn from a point to a circle are always equal, so DF = DB and EF = EC. So regardless of the green tangent’s orientation, the perimeter of triangle ADE is 10 + 10, or 20.

June 9, 2011January 28, 2013 | Puzzles