Given: AB, AC – tangents, B, C – tangency points, angle BAO = 56 degrees, OC = 4 cm. Find: angle OAB, OB.

The length of the OB segment is equal to the length of the OC segment as the radii of the circle.

OB = OS = 4 cm.

The radii OB and OC are drawn to the points of tangency B and C of tangents AB and AC, then the radii OB and OC are perpendicular to tangents AB and AC, and then the triangles AOC and AOB are rectangular.

Tangents AC and AB are drawn from one point A, then, by the property of tangents, AB = AC.

In right-angled triangles AOB and AOC, the hypotenuse of AO is common, leg OB = OS, then triangles AOB and AOC are equal in leg and hypotenuse.

Then the angle ОАВ = ОАС = BAC / 2 = 56/2 = 28.