It is easy to know that point p is the intersection of angle A.B.C and bisector of triangle.

Angle α is the angle of circumference and angle BOC is the angle of center.

Let angle a be x and angle BOC be 2X.

Connecting PB and PC

So: angle B+ angle C= 180- angle a.

Angle PBC+ Angle PCB = 90 Angle α/2

Angle BPC= 180-(90-degree angle A/2)=90 degrees+angle A/2 = 90 degrees+x.

It is impossible to find "angle BOC+ angle BPC=90". Or "angle BOC+ angle BPC= 180". (Note here)

Press "Angle BOC+ Angle BPC= 180" below. A.

So: 90+X+2X= 180.

X=60

Angle A = 60