Question

Хорда делит окружность на части,отношение которых равно 3:7.Найдите углы,которые образует эта хорда с касательной к окружности,проведенной в ее конце

Answer 1

Хорда делит окружность на части,отношение которых равно 3:7.Найдите углы,которые образует эта хорда с касательной к окружности,проведенной в ее конце

Answer 2

Finding the Angles Formed by a Chord and Tangent

To find the angles formed by a chord and a tangent to a circle, we can use the relationship between the intercepted arc and the central angle. Let's denote the intercepted arc by a and the central angle by θ.

Given that the chord divides the circle into two parts with a ratio of 3:7, we can determine the measure of the intercepted arc a. Let's assume the smaller part of the circle has an intercepted arc of length 3x, and the larger part has an intercepted arc of length 7x.

The sum of the intercepted arcs is equal to the circumference of the circle, which is 360 degrees. Therefore, we can set up the following equation:

3x + 7x = 360

Simplifying the equation, we get:

10x = 360

Solving for x, we find:

x = 36

Now that we know the value of x, we can find the lengths of the intercepted arcs:

3x = 3 * 36 = 108 7x = 7 * 36 = 252

So, the smaller intercepted arc is 108 degrees, and the larger intercepted arc is 252 degrees.

To find the angles formed by the chord and the tangent, we need to consider the relationship between the intercepted arc and the central angle. The angle formed by the chord and the tangent is half the measure of the intercepted arc.

Therefore, the angle formed by the chord with the tangent at its end is:

θ = (1/2) * 108 = 54 degrees

And the angle formed by the chord with the tangent at the other end is:

θ = (1/2) * 252 = 126 degrees

So, the angles formed by the chord with the tangent are 54 degrees and 126 degrees.

Please note that the above calculations assume a