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: Understand the properties of a chord bisected by a line from the center. In a circle, a line segment from the center that bisects a chord is perpendicular to the chord. Given that A is the center and AS bisects chord PQ at R, it means that AR is perpendicular to PQ, forming a right angle at R. Also, R is the midpoint of PQ. Step 2: Calculate the length of PR. Since R is the midpoint of PQ and PQ = 48 cm: PR = (PQ)/(2) = (48)/(2) = 24 cm Step 3: Identify the right-angled triangle and apply the Pythagorean theorem. Consider the right-angled triangle ARP. The sides are AR, PR, and AP. AR is given as 7 cm. PR is calculated as 24 cm. AP is the radius of the circle. Let r be the radius. According to the Pythagorean theorem: AP^2 = AR^2 + PR^2 r^2 = 7^2 + 24^2 r^2 = 49 + 576 r^2 = 625 r = sqrt(625) r = 25 cm The length of the radius is 25 cm. That's 2 down. 3 left today — send the next one.