1960 IMO Problems/Problem 4
Construct triangle , given , (the altitudes from and ), and , the median from vertex .
Let , , and be the midpoints of sides , , and , respectively. Let , , and be the feet of the altitudes from , , and to their opposite sides, respectively. Since , with , the distance from to side is .
Construct with length . Draw a circle centered at with radius . Construct the tangent to this circle through . lies on .
Draw a circle centered at with radius . Construct the tangent to this circle through . lies on . Then .
Construct the line parallel to so that the distance between and is and lies between these lines. lies on . Then .
|1960 IMO (Problems)|
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