In the geometric figure, the point p is the center of a circle and the two angles marked are 20 Degree (converted to radians): GeometricScene[{{a, b, c, p}, {r}}, {CircleThrough[{a, b, c}, p], GeometricAssertion[PlanarAngle[{a, b, p}] == \[Pi] 20/180], GeometricAssertion[PlanarAngle[{a, c, p}] == \[Pi] 20/180], GeometricAssertion[PlanarAngle[{b, p, c}] == r]}]; RandomInstance[%, RandomSeeding -> 500] The angle $\angle bpc$ is fully determined by the geometry and must have angle $80^{\circ}$, ...
