If triangle ABC is an equilateral triangle such that AD perpendicular BC then AD2=k(DC)2then find the value of k
Finding the value of k
Given, AD2=k(DC)2
As the triangle is equilateral, ⇒AB=BC=ACAD⊥BC
According to the RHS congruency,
⇒ΔABD≅ΔACDasAB=AC
AD=AD(common)
∠ADB=∠ADC=90°
BD=CD=BC2BC=2CDAC=2CD
Applying the Pythagoras theorem.
AD²=AC²-CD²AD²=(2CD)²-CD²AD²=3CD²
k=3
Hence, the value of k is 3 .