Through a point of a circle of radius r, a tangent and a chord equal to the root of 3. find the angle between them.

Let us mentally connect the center of the circle and the point through which the chord and the tangent are drawn, note to ourselves that this segment forms an angle of 90 ° with the tangent.

Let’s connect the center of the circle and the second and end of the chord in the same way. A triangle where the chord serves as the base is isosceles (its sides are 2 of the radius). That is, if you draw the height in it to the chord, then it will be divided in half. The angle at the base of this triangle plus the desired angle is 90 °, as described above.

Let’s find out what the cosine of the angle at the base of this triangle will be:

r√3 / 2: r = √3 / 2.

According to the table, this corresponds to an angle of 30 °.

Then our desired angle is:

90 – 30 = 60.

Answer: 60 °.