This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution for question 14: a) State the special name of the triangle AOB. Since AB is a diameter and O is the center, points A, O, and B are collinear. OA and OB are both radii, so OA = OB. A triangle with two equal sides is isosceles. Since the points are collinear, it is a degenerate isosceles triangle. b) Find the value of angle AOB. Since AB is a diameter and O is the center, A, O, and B lie on a straight line. The angle on a straight line is 180^. Therefore, AOB = 180^. c) Find the value of angle AOC. The angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the circumference. Arc AC subtends AOC at the center and ABC at the circumference. Given ABC = 30^. AOC = 2 × ABC AOC = 2 × 30^ AOC = 60^ d) If the radius of the circle is 7cm, calculate the length of the arc AC. Step 1: Identify the given values. Radius r = 7 cm. Angle subtended by arc AC at the center, AOC = 60^. Step 2: Use the formula for arc length. The length of an arc L is given by the formula: L = ()/(360^) × 2 r where is the central angle in degrees. Step 3: Substitute the values into the formula. L_AC = (60^)/(360^) × 2 (7 cm) Step 4: Simplify the expression. L_AC = (1)/(6) × 14 cm L_AC = (14)/(6) cm L_AC = (7)/(3) cm That's 2 down. 3 left today — send the next one.