Using the Pythagorean theorem, c = √(a² + b²) = √(6² + 8²) = √(36 + 64) = √100 = 10.

Since the x-coordinates are the same, the distance is the difference in y-coordinates: d = |y2 - y1| = |5 - 2| = 3.

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.

The length of a vertical line segment is the difference in the y-coordinates. Here, length = 7 - 3 = 4.

Using the distance formula: d = √((5 - 0)² + (12 - 0)²) = √(25 + 144) = √169 = 13.

Using the distance formula: d = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.

Length = |y2 - y1| = |7 - 3| = 4.

The length of the median can be calculated using the formula: median = 1/2 * √(2AB^2 + 2AC^2 - BC^2) = 1/2 * √(2*6^2 + 2*8^2 - 10^2) = 7 cm.

Using the area formula A = πr², we set 100π = πr², leading to r² = 100, thus r = 10 cm.

Using the area formula A = πr², we have 36π = πr², thus r² = 36, and r = 6 cm.

Using the area formula A = πr², we have 50 = πr², thus r² = 50/π, and r ≈ 7.07 cm.

The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.

Using the area formula A = πr², we have 36π = πr², which simplifies to r² = 36, giving r = 6 cm.

The area A of a circle is given by A = πr². Therefore, r² = 50, which gives r = √50 = 5√2 cm, approximately 7.07 cm.

Area of a circle = πr². Setting 50π = πr² gives r² = 50, so r = √50 = 5√2 ≈ 7.07 units.

The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.

The area of a square is given by side^2. Thus, if area = 64, then side = √64 = 8.

The diagonal of the square equals the diameter of the circle. Diagonal = 2 × radius = 10. Side = diagonal/√2 = 10/√2 = 5√2.

Length of side = 5 - 1 = 4.

The length of the side is 5 - 1 = 4.

Using the tangent-secant theorem, PT² = PO² - OT². Thus, PT² = 13² - 5² = 169 - 25 = 144, so PT = 12 cm.

The maximum value of a cosine function y = Acos(Bx) is |A|. Here, A = 2, so the maximum value is 2.

The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.

Mean = (1 + 1 + 2 + 3 + 5) / 5 = 12 / 5 = 2.4.

Mean = (12 + 15 + 20 + 25) / 4 = 72 / 4 = 18.

Mean = (15 + 25 + 35 + 45) / 4 = 30.

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3

Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.

The angle formed by a tangent and a chord is equal to half the angle subtended by the chord at the circumference.