Two chords AB and CD of a circle meet at E inside the circle as shown in the figure, such that begin mathsize 12px style EC over AE equals BE over ED equals 1 third end stylebegin mathsize 12px style angle BAC equals 50 degree. space Find space fraction numerator straight A left parenthesis increment AEB right parenthesis over denominator straight A left parenthesis increment DEC right parenthesis end fraction. end style

Asked by Topperlearning User | 5th Oct, 2017, 08:12: AM

Expert Answer:

begin mathsize 12px style angle space BAC space equals space 50 degree space rightwards double arrow space angle space BDC space equals space 50 degree space space space space left parenthesis angles space in space the space same space segment space of space straight a space circle space are space equal right parenthesis
Also comma space we space have comma space angle space AEB space equals space angle space DEC space space space left parenthesis vertically space opposite space angles right parenthesis
and space angle space BAE space equals space angle space CDE space left parenthesis proved space above right parenthesis
So comma space increment space AEB space tilde space increment DEC space space space left parenthesis AA space rule right parenthesis
Hence comma space fraction numerator straight A space left parenthesis increment space AEB right parenthesis over denominator straight A space left parenthesis increment space DEC right parenthesis end fraction space equals space BE squared over AD squared space space space space space space space left parenthesis The space areas space of space two space similar space triangles space are space proportional space to space the
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space squares space of space their space corresponding space sides. right parenthesis
So comma space space fraction numerator straight A space left parenthesis increment space AEB right parenthesis over denominator straight A space left parenthesis increment space DEC right parenthesis end fraction equals open parentheses 1 third close parentheses squared equals 1 over 9 end style

Answered by  | 5th Oct, 2017, 10:12: AM