Geometry Problem

Click the figure below to see the complete problem 559.

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Level: High School, SAT Prep, College geometry

## Wednesday, December 29, 2010

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el angulo entre las bisectrices de dos angulos suplementarios es 90° y aquí, por llegar al incentro, tenemos bisectrices.

ReplyDeleteADB/2 = (B1 + C)/2 and BDC/2 = (180 - B1 - C)/2

ReplyDelete=>

ADB/2 + BDC/2 = 90

I have sent yesterday solution for 558 (delete this )

angle EDB = (1/2)*angle BDA and angle BDF = (1/2)* angle BDC. adding the results we get angle EBD + angle BDF = angle EDF = (1/2)*(angle BDA + angle BDC) = (1/2)*angle ADC = (1/2)*180 degrees = 90 degrees. ADC is a straight line so angle ADC is 180 degrees. therefore angle EDF = 90 degrees.

ReplyDeleteQ. E. D.

Since DF bisects < BFA and EF bisects < CFA the result is obvious

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka