Angles subtended by the same arc at the circumference of a circle are equal.

If two chords are equal in length, they are equidistant from the center of the circle.

Using the intersecting chords theorem: AE * EB = CE * DE, so 3 * 4 = CE * 2, CE = 6 cm.

Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 5 = CE * 4. Therefore, 15 = CE * 4, which gives CE = 15/4 = 3.75 cm.

According to the intersecting chords theorem, the products of the segments of the chords are equal, hence AE * EB = CE * ED.

The measure of each angle formed is equal to the sum of the measures of the arcs intercepted by the angle.

The angles formed by two intersecting chords are equal.

The angles formed by two intersecting chords inside a circle are supplementary.

The lengths of the tangents from a point outside the circle to the circle are equal.

The lengths of the tangents drawn from an external point to a circle are always equal.

There is no mode since all grades appear only once.

Let the number of girls be 2x and boys be 3x. The equation is 2x + 3x = 25. Solving gives 5x = 25, so x = 5. Therefore, girls = 2x = 10.

Mean = (85 + 90 + 75 + 80 + 95 + 70 + 80 + 85 + 90 + 100) / 10 = 85.

Parallel lines have the same slope. Therefore, if line A has a slope of 2, line B also has a slope of 2.

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

Parallel lines have the same slope, so the slope of the parallel line is -1/2.

The slope of line A is -3. The slope of a line perpendicular to it is the negative reciprocal, which is 1/3.

The slope of line A is 1/2. The slope of a line perpendicular to it is the negative reciprocal, which is -2.

Parallel lines have the same slope. Therefore, the slope of line B is also 2.

Parallel lines have the same slope, so the slope of L2 is also 2.

Parallel lines have the same slope. The slope of line L1 is 2, so the slope of line L2 is also 2.

Parallel lines have the same slope. The slope of L1 is 2, so the slope of L2 is also 2.

Parallel lines have the same slope. The slope of the line y = 2x + 3 is 2, so the slope of the parallel line is also 2.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4 units.

The distance between two points with the same x-coordinate is the difference in their y-coordinates: |7 - 3| = 4 units.

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

The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

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.

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.