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
Step 1: Identify properties from the diagram. The figure shows a cyclic quadrilateral ABCD inscribed in a circle with center O. • AB is a diameter because it passes through the center O. • BCD = 110^. • ADC = t. • Chord CD = Chord CB (indicated by the double hash marks). Step 2: Use the property of angles in a semicircle. Since AB is a diameter, the angle subtended by the diameter at any point on the circumference is 90^. Therefore, ADB = 90^. Step 3: Use the property of opposite angles in a cyclic quadrilateral. In a cyclic quadrilateral, opposite angles sum to 180^. DAB + BCD = 180^ Substitute the given value for BCD: DAB + 110^ = 180^ DAB = 180^ - 110^ = 70^ Step 4: Use the property of equal chords. Given that chord CD = chord CB. Equal chords subtend equal angles at the circumference. This means the angles subtended by these chords at any point on the remaining part of the circumference are equal. Specifically, CAD (subtended by chord CD) is equal to CAB (subtended by chord CB). So, CAD = CAB. Since $ DAB = CAD + \