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 of triangle ABC. Given that |AB| = |AC|, triangle ABC is an isosceles triangle. The base angles opposite the equal sides are equal, so ABC = ACB. The sum of angles in a triangle is 180^. We are given BAC = 2x^. Therefore, ABC + ACB + BAC = 180^ 2 ABC + 2x^ = 180^ 2 ABC = 180^ - 2x^ ABC = (180^ - 2x^)/(2) ABC = (90 - x)^ Step 2: Apply the Alternate Segment Theorem. The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. In this figure, AD is the tangent to the circle at point A, and AC is a chord through the point of contact A. The angle between the tangent AD and the chord AC is DAC. The angle in the alternate segment subtended by the chord AC is ABC. According to the theorem, these angles are equal: DAC = ABC Step 3: Calculate DAC. Substitute the value of ABC found in Step 1 into the equation from Step 2: DAC = (90 - x)^ Comparing this result with the given options, it matches option D. The final answer is D. (90 - x)^. Send me the next one 📸