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Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 1018.
Consider angle CBD as X ---> angle BAC = 2X (tangents rule)Consider angle ABE as Y ---> angle BCA = 2Y (tangents rule)From here we can see in triangle ABC that 2X + 2Y = 90 --> X+Y = 45In triangle BDE we get :angle BDE = 2Y + Xangle BED = 2X + Yangle BDE + angle BED = 3Y + 3X = 135 THUS DBE = 45
<ABE=<BCE/2, and <CBD=<BAD/2, so <EBD=90-<ABE-<CBD=90-(<BCE/2+<BAD/2)=90-90/2=45
3 Angles of Tr. BED =< ABC + 2.<EBD. Hence < EBD = 90/2= 45Sumith PeirisMoratuwaSri Lanka