AB and AD are two tangents to some circle of radius 5 cm (B and D are tangency points) point C belongs

AB and AD are two tangents to some circle of radius 5 cm (B and D are tangency points) point C belongs to the largest of the arcs ВD. Find the angle of the ВСD if AB is 5 cm.

From point O, the center of the circle, draw the radii OB and OD to the points of tangency.

By the property of tangents, the radii drawn to the point of tangency are perpendicular to the tangents, then the angles ABO and ADO are straight.

In a quadrangle ABOD, OD = OB as the radii of a circle, AB = OB by condition, then the quadrilateral ABOD is a square. Then the central angle BOD is equal to 90. The degree measure of the BD arc is equal to the degree measure of the central angle BOD, then the inscribed angle BCD is equal to half the degree measure of the arc BD on which it rests. Angle ВСD = 90/2 = 45.

Answer: The BCD angle is 45.