Question

Two circles each of which passes
through the centre of the other,
intersect at points M and N . A
line from m intersects the circle at
k and L as shown in fig. if KL
= 6. Compute the area of triangle KLN
​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

9√3  

Step-by-step explanation:

Lets join OQ

now

OQ = Radius  ON = NQ = OM = QM = Radius

ΔOQN & ΔOQM are equilateral triangle

hence

Chord MN Subtending angle 120° at O & Q

=>  ∠KLN = ∠MLN = (1/2) 120° = 60°

now if we extend LN till point X on circle & Join MX

=> ∠MXN =  (1/2) 120° = 60°

now K N X M lies on a circle hence KNXM is a cyclic Quadrilateral

=> ∠MKN + ∠MXN = 180°

=> ∠MKN = 120°

∠MKN = ∠KNL + ∠KLN

=> 120° = ∠KNL + 60°

=>  ∠KNL = 60°

=> Δ KLN is Equilaterla triangle

with KL = 6

Area = (√3 / 4) * 6² = 9√3