Radius = distance from center to point = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √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.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (6/9)² = (2/3)² = 4/9.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (6/9)² = (2/3)² = 4/9.

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.

Using the Pythagorean theorem, a² + b² = c², we have 3² + b² = 5², which gives b² = 25 - 9 = 16, so b = 4 units.

The slope m = (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

The ratio of the sides is 6/3 = 2. Therefore, the corresponding sides are 6*2, 4*2, and 5*2, which are 6, 8, and 10 units.

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (60/360) * 2π(6) = (1/6) * 12π = 2π units.

Using the Pythagorean theorem, the diagonal d = √(width² + height²) = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

Area = πr², so 50π = πr². Thus, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.

Arc length = rθ, where θ is in radians. Thus, 10 = 5θ, so θ = 2 radians. Converting to degrees: θ = 2 * (180/π) ≈ 114.6 degrees.