Given that A is the center and AS bisects chord PQ at R, it means that AR is perpendicular to PQ, forming a…

Question

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.

ScanSolve AI Tutor · Accepted 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: AP² = AR² + PR²; r² = 7² + 24²; r² = 49 + 576; r² = 625; r = √(625); r = 25 cm The length of the radius is 25 cm.

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.

Step-by-step solution

Understand the properties of a chord bisected by a line from the center.

Calculate the length of PR.

Identify the right-angled triangle and apply the Pythagorean theorem.

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