The correct option is B inside the circle
The distance between two points (x1,y1) and (x2,y2) is √(x2−x1)2+(y2−y1)2.
So, the radius of the circle = Distance between (1, 5) and (6, -7)
The radius of the circle = √(6−1)2+(−7−5)2
The radius of the circle = √(5)2+(−12)2
The radius of the circle = √25+144
The radius of the circle = √169
The radius of the circle = 13 units
Distance between (1, 5) and (-7, -1) = √(−7−1)2+(−1−5)2
Distance between (1, 5) and (-7, -1) = √(−8)2+(−6)2
Distance between (1, 5) and (-7, -1) = √64+36
Distance between (1, 5) and (-7, -1) = √100
Distance between (1, 5) and (-7, -1) = 10 units
So, the distance between (1, 5) and (-7, -1) is less than the radius of the circle.
Hence, point (-7, -1) lies inside the circle.