The angle between the diameter AB and the chord AC of the circle is 40 degrees. A tangent line to a circle

The angle between the diameter AB and the chord AC of the circle is 40 degrees. A tangent line to a circle is drawn through point C, which intersects line AB at point B. Determine the type of triangle ACD

Let us draw the radius of the OС to the point of contact C, then the triangle AOС is isosceles since OA = OС = R, and the angle OAС = OСA = 40.

By the property of the tangent to the circle, the radius of the OS drawn to the point of tangency is perpendicular to the tangent CD, then the angle ACD = ACO + OСD = 40 + 90 = 130.

Angle ADC = 180 – CAD – ACD = 180 – 40 – 130 = 10.

Answer: The ACD triangle is obtuse.