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angle wanted, altitudes of 2 trianlges related (2018 Kyiv City MO 10.4 )

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September 12, 2020
geometryanglesaltitudes

Problem Statement

In the acute-angled triangle ABCABC, the altitudes BPBP and CQCQ were drawn, and the point TT is the intersection point of the altitudes of ΔPAQ\Delta PAQ. It turned out that ∠CTB=90∘\angle CTB = 90 {} ^ \circ. Find the measure of ∠BAC\angle BAC.
(Mikhail Plotnikov)
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