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Find the angle

Source: MTRP 2019 Class 11-Multiple Choice Question: Problem 4 :-

April 9, 2020
geometry

Problem Statement

Suppose △ABC\triangle ABC is a triangle. From the vertex AA draw the altitude AHAH, angle bisector (of ∠BAC\angle BAC) APAP, median ADAD and these intersect the side BCBC at the points (from left in order) HH, PP, DD respectively. Let ∠CAH=∠HAP=∠PAD=∠DAB\angle CAH = \angle HAP = \angle PAD = \angle DAB. Then ∠ACH=\angle ACH =
[*] 22.5∘22.5^{\circ} [*] 45∘45^{\circ} [*] 67.5∘67.5^{\circ} [*] None of the above
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