From point K, not lying on the circle with center O, 2 tangents are drawn, they intersect with the circle at points M and N.

From point K, not lying on the circle with center O, 2 tangents are drawn, they intersect with the circle at points M and N. The distance from K to the center O is 15 cm, and the radius of the circle is 7.5 cm. Find what is the angle MKN.

KM = KN and angle MKO = angle NKO – since the segments of the tangents to the circle, which are drawn from one point, are equal, the angles between the straight line that passes through this point and the center of the circle are also equal.
MO = NO = 7.5cm.
Angle KMO = Angle KNO = 90 degrees since tangents are perpendicular to the radius drawn to the tangent point.
Triangles KMO and KNO are equal right-angled triangles.
Find the sine of the CIE angle. The sine of an angle in a right-angled triangle is the ratio of the opposite leg to the hypotenuse:
sinMKO = MO / KO;
sinMKO = 7.5 / 15 = 1/2.
sinMKO = sinNKO = 1/2.
1/2 is the sine of an angle of 30 degrees, then angle MKO = angle NKO = 30 degrees.
Angle MKN consists of two angles MKO and NKO, then:
MKN = MKO + NKO;
MKN = 30 + 30 = 60 (degrees).
Answer: MKN = 60 degrees.