Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1171.
I use subscript 1 2 3 instead. Since K = 1/2 ah₁ = 1/2 bh₂ = 1/2 ch₃a = 2K/h₁b = 2K/h₂c = 2K/h₃Substitude into the result of the last problem, done.
Let p, q, r be the reciprocals of the altitudes drawn from A, B, C respectively.So a = 2Kp, b = 2Kq and c = 2KrPer the result of Problem 1170 and my proof therein16K^2,= 2a^2b^2 + 2b^2c^2 + 2c^2a^2 - a^4- b^4 - c^4 = (a+b+c)(a+b-c)(a-b+c)(-a+b+c) where I have used the difference between 2 squares to simplify the algebraThis is = to 16K^4 (p+q+r)(p+q-r)(p-q+r)((-p+q+r) from which the result follows by dividing both sides of the equation by 16K^4 and taking the reciprocal and then the square root of both sides Sumith PeirisMoratuwaSri Lanka