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?

1 Answer
Feb 9, 2018

Answer:

#BD = CD = color(green)(4# #color(green)(cm#

Explanation:

Given AB = AC, BD = 4 cm. Also AB is the diameter of the circle with D on the circumference.

Construction : Join AD

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In triangle ABD, #AhatDB =90^0# as angle in a semicircle is a right angle.

#AB^2 = AD^2 + BD^2# Eqn (1)

Now let us consider triangle ACD.

#AhatDC = 90^0# as #AhatDB =90^0#

Therefore, #AC^2 = AD^2 + CD^2# Eqn (2)

Compare equations (1) & (2),

Given : AB = AC

#:. cancel(AD^2) + BD^2 = cancel(AD^2) + CD^2#

#BD^2 = CD^2# or #BD = CD = 4# cm