Question

Касательная к окружности с центром 0 в точках M и N пересекаются в точке P найдите MPN если угол MON равен 142 ответ дайте в градусах

Answer 1

∠MON является центральным углом, поэтому ∪ MN=124°. Угол между касательной (РМ и РN) и хордой (MN) равен половине градусной меры дуги, которую он стягивает.Поэтому ∠MPN=124:2=62°

Answer 2

Problem Analysis

We are given a circle with center O, and two tangents to the circle from points M and N. The tangents intersect at point P. We need to find the measure of angle MPN, given that angle MON is 142 degrees.

Solution

To find the measure of angle MPN, we need to determine the relationship between angle MPN and angle MON.

Since the tangents from points M and N are drawn to the circle, we know that the tangents are perpendicular to the radii drawn from the center of the circle to the points of tangency. Therefore, angle MON is a right angle.

Since angle MON is 142 degrees and it is a right angle, we can subtract 90 degrees from 142 degrees to find the measure of angle MPN.

Let's calculate the measure of angle MPN:

142 degrees - 90 degrees = 52 degrees

Therefore, the measure of angle MPN is 52 degrees.

Conclusion

The measure of angle MPN, given that angle MON is 142 degrees, is 52 degrees.