Given circle X with radius 5 units and chord AB with length 8 units, what is thelength of segment XC, which bisects the chord?
Accepted Solution
A:
Answer: The correct option is (B) 3.Step-by-step explanation: We are given a circle X with radius 5 units and chord AB with length 8 units.We are to find the length of segment XC that bisects chord.We know that the line segment drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.So, in the given circle X, the segment XC is perpendicular to chord AB. Then, triangle XCB will be a right angled triangle with hypotenuse XB.Since XC bisects AB, so the length of BC will be[tex]BC=\dfrac{AB}{2}=\dfrac{8}{2}=4~\textup{units}.[/tex]And, radius, XB = 5 units.Using Pythagoras theorem in triangle XCB, we have[tex]XB^2=XC^2+BC^2\\\\\Rightarrow XC^2=XB^2-BC^2\\\\\Rightarrow XC^@=5^2-4^2\\\\\Rightarrow XC^2=9\\\\\Rightarrow XC^2=3^2\\\\\Rightarrow XC=3.[/tex]Thus, the length of the segment XC is 3 units.Option (B) is CORRECT.