Bisectors

fahad nasir · August 12th, 2018, 05:08 AM

ABC is a triangle B' is a point in AC such that BB' is a bisector of the angle B, similarly CC' is the bisector of the angle C. Show that m(A)= 60 degree if and only if BC=BC'+CB'.

skipjack · August 13th, 2018, 06:24 AM

m(A) = 60 degrees if and only if AC² + AB² = BC² + AB.AC.

Use the angle bisector theorem to show that BC = BC' + CB' if and only if AC² + AB² = BC² + AB.AC.

August 12th, 2018, 05:08 AM	#1
fahad nasir Member Joined: Oct 2012 Posts: 71 Thanks: 0	Bisectors ABC is a triangle B' is a point in AC such that BB' is a bisector of the angle B, similarly CC' is the bisector of the angle C. Show that m(A)= 60 degree if and only if BC=BC'+CB'.
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August 13th, 2018, 06:24 AM	#2
skipjack Global Moderator Joined: Dec 2006 Posts: 20,293 Thanks: 1968	m(A) = 60 degrees if and only if AC² + AB² = BC² + AB.AC. Use the angle bisector theorem to show that BC = BC' + CB' if and only if AC² + AB² = BC² + AB.AC.
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