What does Angle ABC Equal?Date: 5 Mar 1995 13:07:10 -0500 From: Vivien Cumyn Subject: Triangle problem Ok, I've got a real whopper of a problem, A triangle, ABC, is obtuse angled at C. The bisectors of the exterior angles at A and B meet BC and AC produced at D and E respectively. If AB =AD =BE, then angle ABC is equal to ? Date: 5 Mar 1995 16:53:13 -0500 From: Dr. Ken Subject: Re: Triangle problem Hello there! I'll see if I can give you a few hints, without actually solving the problem for you. 1) since AB = AD = BE, triangles DAB and ABE are isosceles, so angle DBA = BDA, and angle EAB = AEB. 2) Draw your picture with AB horizontal and C below it. Notice that there was no asymmetrical information in the problem, meaning that whatever we constructed on the left side we also constructed on the right side and vice versa. So you can probably assume that angle CAB = CBA, which will greatly reduce the complexity of the calculations, since you can use the same variable to represent each of them. See if you can tackle it now, with these things in mind. If you can't, write back and we'll help you out some more. -Ken "Dr." Math |
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