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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve second part from which masses start 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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