# 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?

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

In triangle ABD, $A \hat{D} B = {90}^{0}$ as angle in a semicircle is a right angle.

$A {B}^{2} = A {D}^{2} + B {D}^{2}$ Eqn (1)

Now let us consider triangle ACD.

$A \hat{D} C = {90}^{0}$ as $A \hat{D} B = {90}^{0}$

Therefore, $A {C}^{2} = A {D}^{2} + C {D}^{2}$ Eqn (2)

Compare equations (1) & (2),

Given : AB = AC

$\therefore \cancel{A {D}^{2}} + B {D}^{2} = \cancel{A {D}^{2}} + C {D}^{2}$

$B {D}^{2} = C {D}^{2}$ or $B D = C D = 4$ cm