Q26 of 180 Page 5

In an equilateral

Theorem: Altitude of an equilateral triangle bisects the corresponding side.

Therefore, BD = CD =1/2 a

Now, in ΔADC,

AD = h cm

CD = 1/2 a cm

AC = a cm

Applying the Pythagoras theorem, we get,

AC² = AD² + CD²

a² = h² + (a/2)²

Hence, Proved.

In the figure below, the incircle of ΔPQR touches the sides QR, RP and PQ at K, L and M respectively. If PQ = PR, prove that KQ = KR