Using the formula: chord length = 2√(radius² - distance from center²). Here, chord length = 2√(10² - 8²) = 2√(100 - 64) = 2√36 = 12.

Using the Pythagorean theorem, the length of the tangent is √(15^2 - 10^2) = √(225 - 100) = √125.

Using the tangent length formula: length = √(distance from center² - radius²) = √(15² - 10²) = √(225 - 100) = √125 = 5√5 ≈ 11.18.

Using the formula: chord length = 2 * √(radius² - distance from center²) = 2 * √(7² - 4²) = 2 * √(49 - 16) = 2 * √33 ≈ 11.55.

Area = (1/2) * base * height, so 30 = (1/2) * 10 * height. Thus, height = 6.

Area = (1/2) * base * height, so 30 = (1/2) * 5 * height. Thus, height = 30 * 2 / 5 = 12.

The side opposite the 30-degree angle is half the hypotenuse: 10 * 1/2 = 5.

Using the Pythagorean theorem, b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12.

Using the Pythagorean theorem, b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12.

In a 30-60-90 triangle, the hypotenuse is twice the shortest side. Therefore, hypotenuse = 2 * 5 = 10.

Using the Pythagorean theorem, check if 25² = 7² + 24². 625 = 49 + 576, which is true. Thus, it is a right triangle.

Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Here, radius² = 6² + (16/2)² = 36 + 64 = 100, so radius = √100 = 10.

Using the formula d = √(r^2 - (c/2)^2), where r = 10 and c = 16, we get d = √(10^2 - 8^2) = √(100 - 64) = √36 = 6.

Using the formula d = √(r^2 - (c/2)^2), where r is the radius and c is the length of the chord: d = √(10^2 - (16/2)^2) = √(100 - 64) = √36 = 6.

Using the formula: distance = √(radius² - (half of chord length)²) = √(10² - (16/2)²) = √(100 - 64) = √36 = 6.

A radius that bisects a chord is perpendicular to the chord.

Using the formula: chord length = 2 * √(radius² - distance from center²) = 2 * √(5² - 4²) = 2 * √(25 - 16) = 2 * √9 = 6.

Using the tangent length formula: length = √(distance from center² - radius²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Using the Pythagorean theorem, b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

In a 30-60-90 triangle, the ratio of the opposite side to the hypotenuse is 1:2.

The angle between a tangent and a chord at the point of contact is always 90 degrees.

The angle formed between the tangent and the chord is equal to the angle subtended by the chord at the center of the circle.

The angle between the chord and the radius at the point of tangency is equal to the angle between the tangent and the chord, which is 30 degrees. Therefore, the angle between the chord and the radius is 90 - 30 = 60 degrees.

Check using the Pythagorean theorem: 25² = 7² + 24², 625 = 49 + 576, 625 = 625. It is a right triangle.

Using the Pythagorean theorem, c = √(12² + 16²) = √(144 + 256) = √400 = 20.

Using the Pythagorean theorem, c = √(8² + 15²) = √(64 + 225) = √289 = 17.

Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15. Perimeter = 9 + 12 + 15 = 36.

A right triangle with equal legs is an isosceles triangle.

Since 5² + 12² = 13², it is a right triangle.

Check using the Pythagorean theorem: 15² = 9² + 12², 225 = 81 + 144, 225 = 225. It is a right triangle.