In isosceles triangle ABC, AB=AC; a circle drawn taking AB as diameter meets the side BC at the point D. IF BD=4cm,let us find the value of CD?

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Answer 1 · 2018-06-01T12:32:04

#color(blue)(CD=4cm)#

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If #AB# is the diameter of the circle, the radius is #1/2AB#

From diagram:

#EB=ED=1/2AB#

#DeltaEBD~DeltaABC#

Therefore:

#|EB|/|BD|=|AB|/|BC|=|1/2AB|/4=|AB|/|BC|#

#|BC|=|4AB|/|1/2AB|=8#

#CD=CB-BD=8-4=4#

#CD=4cm#