Question

14. In adjoining figure, O is a point in the interior of a square ABCD such that
OAB is an equilateral triangle. Show that OD = OC.

Answer 1

Answer:

ΔOAB is equilateral triangle then

ln ΔAOD and ΔBOC

AD=BC (sides of the square)

∠DAO=∠CBD=30  

0

 (90  

0

−angleofequilateralΔ(60  

0

))

AO=OB (sides of equilateral of triangle)

ΔAOD≅ΔBOC (SAS criterion)

then OD=OC

So ΔCOD is an isosceles triangle

Answer 2

Answer:

We know that diagonals of square are equal. Therefore, OD=OC