Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.
Click the diagram below to enlarge it.
Thursday, December 4, 2014
Geometry Problem 1066: Triangle, Obtuse Angle, Orthocenter, Circumradius, Inradius, Exradius, Distance, Diameter
Subscribe to:
Post Comments (Atom)
Since ΔABC and ΔHBC have the same circumradius,
ReplyDeletea₁ = 2R cosH = −2R cosA
r = 4R sin(A/2) sin(B/2) sin(C/2)
r₁ = 4R sin(A/2) cos(B/2) cos(C/2)
r₁ − r = 4R sin(A/2) cos(B/2 + C/2)
= 4R sin²(A/2) = 2R(1−cosA) = 2R + a₁
a₁ + r₁ − r = 2R
r₁ − a₁ = 2R + r