A triangle ABC with incentre O has its incircle touching it at points K, L and M on AB, BC and CA respectively. A line throough B parallel to KL meets MK and LM extended at R and S respectively. Prove that angle ROS is acute.
I have the diagram too. If you need it, give me your email ID and I'll send you an attachment with the diagram.
2006-12-29 15:10:20 · 6 answers · asked by Akilesh - Internet Undertaker 7 in Science & Mathematics ➔ Mathematics
Yahoo doesn't allow diagrams to be posted with the question. It is part of spam protection. I can't provide a link as I didn't get this problem on a website. It is part of 'Practice Problems(Unsolved)' in a training book I purchased.
2006-12-29 22:11:20 · update #1
In the limiting case where triangle ABC, where AB = BC = 1, and where
CA -> 0, lines AB and BC approach being parallel, so that lines KL and LM approach being orthogonal. The center of the circle being inside of the triangle RMS which approaches being a right triangle, we see that triangle ROS must be acute. QED.
2006-12-29 16:34:17 · answer #1 · answered by Scythian1950 7 · 0⤊ 0⤋
A line through B?
2006-12-29 23:20:33 · answer #2 · answered by RS 4 · 0⤊ 0⤋
I set this up in Geometer's Sketchpad. I found that angle ROS is NOT always acute.
2006-12-30 06:02:11 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
cant giv my mail id but i guess u can attach the diagram n post the question
once more
2006-12-29 23:38:27 · answer #4 · answered by Anonymous · 0⤊ 0⤋
sorry need a picture, to see what you mean
2006-12-29 23:18:21 · answer #5 · answered by angel-de-amor 1 · 0⤊ 0⤋
that sounds easy.is that ur homework?
2006-12-29 23:52:18 · answer #6 · answered by goodgirl 1 · 0⤊ 0⤋