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

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 BD. Find the angle BCD if AB = 5cm.

Tangents AB and AD form right angles with radii OB and OD, by the property of tangents to the circle.

Since AB = 5 cm, then AD = 5 cm, since the tangents are drawn to one point. By condition, OB = OD = R = 5 cm.

Then in the rectangle ABO all four sides are equal to 5 cm, and the angles ABO = ADO = 90, then the quadrangle ABO is square, and the central angle BOD = 90.

The angle BOD rests on the smaller arc BD, then its degree measure is also 90. The inscribed angle BCD also rests on the arc BD, which means that it is equal to half of the degree measure of the arc BD. Angle ВСD = 90/2 = 45.

Answer: The BCD angle is 45.