From a point outside the circle, two secants are drawn, the angle between which is 32 degrees.

From a point outside the circle, two secants are drawn, the angle between which is 32 degrees. The large arc bounded by these secants is 100 degrees. What is the smaller arc bounded by these secants?

Let’s build a chord CD.

The inscribed angle ВDC rests on the arc ВС, the degree measure of which, according to the condition, is equal to 100, then the angle ВDC = 100/2 = 50.

The BDC angle is adjacent to the ADC angle, the sum of which is 180, then the ADC angle = (180 – 50) = 130.

Consider triangle ACD. The sum of the interior angles of the triangle is 180, then the angle ACD = (180 – 32 – 130) = 18.

The inscribed angle DCE rests on the arc DE, then the degree measure of the arc DE is 2 * 18 = 36.

Answer: The smaller arc bounded by the secants is 36.