March School Holiday

The school holiday starts, but it is not a time to relax. With the Cuti Terancang homework and a lot of revision to do, my holiday turns out to be schooling at home. However, I am quite lazy and I doubt that I will be able to complete my homework on time. XD

Need to push myself harder! Good Luck!

(This is Taylor Swift in Vogue February 2012 edition. Isn't she beautiful?)

IMO 2011 Question 6

Let ABC be an acute triangle with circumcircle Γ. Let ℓ be a tangent line to Γ, and let ℓa, ℓb andℓc be the lines obtained by reflecting ℓ in the lines BC, CA and AB, respectively

Show that the circumcircle of the triangle determined by the lines ℓa, ℓb and ℓc is tangent to the circle Γ.

Can anyone help me to solve this question?