In a A B C, if ∠ A=60^∘ and the altitudes from B and C meet A C and A B atand Q, respectively and...

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In a A B C, if ∠ A=60^∘ and the altitudes from B and C meet A C and A B atand Q, respectively and intersect each other at I.
(i) Prove that A P I Q and P Q B C are cyclic quadrilaterals.
(ii) Find the measure of ∠ B I C.

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