Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B, and C intersect in points M, N, and P. Find measures of angles of the △MNP.

x = 8

Step-by-step explanation:

The line segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

= ( cross- multiply )

6x(11x - 4) = 63x² ← distribute left side

66x² - 24x = 63x² ( subtract 63x² from both sides )

3x² - 24x = 0 ← factor out 3x from each term on the left side

3x(x - 8) = 0

Equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 8 = 0 ⇒ x = 8

But x > 0 , then x = 8