Chapter 3.8, Problem 13PSB

To determine

If CD is drawn, $\Delta BCD$ will be isosceles is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle ABC\cong \angle ABD={90}^0$

  $\overrightarrow{AC}\cong \overrightarrow{AD}$

  $\overrightarrow{AB}\cong \overrightarrow{AB}$ (common chord)

Formula used : Pythagoras theorem is used, with states that in right angled triangle ABC, if AB is the hypotenuse, then

  $a^2+b^2=c^2$

Proof : In the triangles ABC and ABD, we can apply Pythagoras theorem, thus we get :

  $\overrightarrow{BC}\cong \overrightarrow{BD}$

Now, we can say that in triangle BCD, as $\overrightarrow{BC}\cong \overrightarrow{BD}$ , it will be isosceles.

Hence, the given statement is proved