The chord km is drawn in a circle centered on o. Find the unknown angles of the OKM triangle if the angle KOM = 52 °.

KM – chord. A chord is a segment that connects any two points of a circle, but does not pass through the center (otherwise it will become a diameter). O – center. We were given an OKM triangle. We get that points K and M are connected to the center of the circle. What do we get? That’s right, two radii (KO and MO). We know that it is impossible to draw two different radii in a circle (meaning along the length). That is, in the CIE triangle, two sides are equal. If a triangle has two sides equal, then it is isosceles. We get that, according to the theorem of a p / b triangle, the angles of the MCO and OMC are equal (angles at the base).
Knowing that the remaining third angle = 52 degrees, compose and solve the equation. (we take the fact that the sum of the angles of any triangle = 180 degrees)
x + x + 52 = 180
2x + 52 = 180
2x = 128
x = 128: 2
x = 64
Answer: the remaining angles of the RCM and the OMK are 64 degrees each.