The angle formed by the tangent and the chord is equal to the angle subtended by the chord at the opposite arc.

The tangent to a circle at any point is perpendicular to the radius at that point, forming a 90-degree angle.

Since PT is perpendicular to OT, PT is equal to the radius OT, which is 5 cm.

The radius drawn to the point of tangency is perpendicular to the tangent line at that point.

The length of the tangent PT from point P to the point of tangency T is equal to the radius OT, which is 6 cm.

The tangent to a circle at any point is perpendicular to the radius drawn to the point of tangency.

The tangent to a circle at any point is perpendicular to the radius drawn to the point of contact.

The tangent to a circle at any point is perpendicular to the radius drawn to the point of contact, hence the angle is 90 degrees.

$25 - $10 = $15 left.

$20 - $15 = $5

Vertically opposite angles are equal, so the angle is also 40 degrees.

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

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

The interior angles on the same side of the transversal are supplementary, summing to 180 degrees.

The area of a trapezoid is calculated using the formula (1/2) × (base1 + base2) × height. Therefore, area = (1/2) × (10 cm + 6 cm) × 4 cm = 32 cm².

The length of the midsegment of a trapezoid is the average of the lengths of the two bases. Midsegment = (8 + 12) / 2 = 10 cm.

height = shadow * tan(45°) = 10 * 1 = 10 meters

Area = 1/2 * base * height = 1/2 * 15 * 10 = 75 cm².

Area = 1/2 × base × height = 1/2 × 5 cm × 3 cm = 7.5 cm².

Area = 1/2 × base × height = 1/2 × 5 cm × 4 cm = 10 cm².

Area = 1/2 x base x height = 1/2 x 6 x 4 = 12 cm²

Area = 1/2 * base * height; 24 = 1/2 * 8 * height; height = 6 cm.

Area = 1/2 * base * height. 36 = 1/2 * 9 * height. Height = (36 * 2) / 9 = 8 cm.

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

The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 50 - 60 = 70 degrees.

A triangle with sides a, b, and c (where c is the longest side) is a right triangle if a² + b² = c². Here, 5² + 12² = 25 + 144 = 169 = 13², so it is a right triangle.

The perimeter of a triangle is the sum of its sides: 6 + 8 + 10 = 24 cm.

This triangle is a right triangle because it satisfies the Pythagorean theorem: 6^2 + 8^2 = 10^2 (36 + 64 = 100).

This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).

Perimeter = AB + BC + CA = 3 + 3 + 4 = 10.