Presentation on theme: "Tangent Circles Finding solutions with both"— Presentation transcript:
1 Tangent Circles Finding solutions with both Law of Cosines and Stewart’s TheoremInspired by(though not actually stolen from)problem #10 on the2011 High School Purple Comet CompetitionWith thanks to Luke Shimanuki for sharing his solution
10 Allows you to calculate the length of a cevian. Stewart’s TheoremAllows you to calculate the length of a cevian.A cevian is a line segment that extends from a vertex of a polygon to it’s opposite side.Medians and altitudes are examples of “special” cevians in a triangle. The formula is:
11 We can rewrite the formula in a way that is easier to remember … Stewart’s TheoremA cevian is a line segment that extends from a vertex of a polygon to it’s opposite side.We can rewrite the formula in a way that is easier to remember …A man and his dad put a bomb in the sink ….
12 Let’s plug our values in and see what we get Stewart’s TheoremLet’s plug our values in and see what we geta =b =c =d =m =n =3r + 2r + 13 – r21
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