Bisectors

fahad nasir · August 12th, 2018, 04:08 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, 05:24 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, 04:08 AM	#1
fahad nasir Member Joined: Oct 2012 Posts: 63 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'.
$fahad nasir is offline$

August 13th, 2018, 05:24 AM	#2
skipjack Global Moderator Joined: Dec 2006 Posts: 19,291 Thanks: 1683	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.
$skipjack is online now$

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
angle bisectors -open problem?	zeta275	Geometry	1	November 10th, 2017 06:14 PM
triangle feet of bisectors	mared	Geometry	2	April 2nd, 2014 02:16 PM