The area of a circle is given by the formula A = πr². Thus, A = π(4)² = 16π.

The circumference of a circle is given by the formula C = 2πr. Therefore, C = 2π * 4 = 8π units.

Using the point-slope form: y - 5 = -3(x - 2). Solving for y gives y = -3x + 11, so the y-intercept is 11.

The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (7 - 3) / (2 - 2), which is undefined since the denominator is 0.

If alternate exterior angles are equal, the lines are parallel.

Interior angles on the same side of the transversal are supplementary, so 180 - 45 = 135 degrees.

Alternate interior angles are equal, so the alternate interior angle is also 30 degrees.

Corresponding angles are equal when two parallel lines are cut by a transversal.

Alternate interior angles are equal when two parallel lines are cut by a transversal.

The slopes of perpendicular lines are negative reciprocals. Therefore, the slope is -1/4.

Vertical angles are equal, so the other pair of vertical angles also measures 120 degrees.

If the ratio of similarity is 2:1, then the sides of the second triangle are 2 times the sides of the first triangle: 3*2, 4*2, 5*2 = 6, 8, 10.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Thus, distance = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5 units.

Using the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 60) = 70 degrees.

Since all angles are less than 90 degrees, the triangle is acute.

The slope of a line perpendicular to another is the negative reciprocal. The negative reciprocal of -3 is 1/3.

Corresponding angles are equal when a transversal intersects two parallel lines.