Circle c has its center at (9,0) and a point is on the circle at a(8,6).
which answer verifies whether point p(10,−7) lies on the circle?

the equation (9−8)2+(0−6)2=(9−10)2+(0+7)2 is a true statement, so p is on ⨀c.
the statement (9−8)2+(0−6)2≠(9−10)2+(0+7)2 is a true statement, so p is not on ⨀c.
the statement (9−0)2+(8−6)2≠(9−0)2+(10+7)2 is a true statement, so p is not on ⨀c.
the equation (9−0)2+(8−6)2=(9−0)2+(10+7)2 is a true statement, so p is on ⨀c.

The answer to your question is the second option is correct

Step-by-step explanation:

Data

C (9, 0)

A (8, 6)

P (10, -7)

Equation

             (x - h)² + (y - k)² = r²    or

             (x₁ - h)² + (y₁ - k)² = (x₂ - h)² + (y₂ - k)²

Substitution

                (8 - 9)² + (6 - 0)² = (10 - 9)² + (-7 - 0)²

Simplification

                (-1)² + (6)² = (1)² + (-7)²

                 1 + 36 = 1 + 49

                       37 ≠ 50               This is a false statement                          

step-by-step explanation:

this is not possible to solve with the info given.   you need at least an one angle somewhere.