Problem 9. Consider a triangle and its inscribed circle. Join each vertex with the point of tangency at the opposite side. Prove using Ceva's theorem that three lines you constructed pass through one point. Which masses need to be placed at the vertices so that their center of mass is the intersection point of these lines. You can express these masses using the lengths of the sides of the triangle AB = c, AC = b, BC = a and basic trigonometric functions of its angles ZBAC = a, ZCBA = 3, ZACB = y.

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Solve second part from masses need to

Problem 9. Consider a triangle and its inscribed circle. Join each
vertex with the point of tangency at the opposite side. Prove using
Ceva's theorem that three lines you constructed pass through one point.
5
Which masses need to be placed at the vertices so that their center of
mass is the intersection point of these lines. You can express these
masses using the lengths of the sides of the triangle AB = c, AC =
b, BC = a and basic trigonometric functions of its angles ZBAC =
a, ZCBA= B, ZACB = 7.
Transcribed Image Text:Problem 9. Consider a triangle and its inscribed circle. Join each vertex with the point of tangency at the opposite side. Prove using Ceva's theorem that three lines you constructed pass through one point. 5 Which masses need to be placed at the vertices so that their center of mass is the intersection point of these lines. You can express these masses using the lengths of the sides of the triangle AB = c, AC = b, BC = a and basic trigonometric functions of its angles ZBAC = a, ZCBA= B, ZACB = 7.
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