Answer:
D) 24 in
Step-by-step explanation:
Line segment QR serves as the median of triangle QOP as it is drawn from vertex Q to the midpoint of side OP. As QR is perpendicular to OP, it divides triangle QOP into two congruent right triangles. To find the length of QR, we can use the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle:
[tex]QR^2+RP^2=QP^2[/tex]
As point R is the midpoint of OP, and OP = 20 in, then RP = 10 in. Therefore, substitute RP = 10 in and QP = 26 in into the equation and solve for QR:
[tex]QR^2+10^2=26^2\\\\QR^2+100=676\\\\QR^2=576\\\\QR=\sqrt{576}\\\\QR=24[/tex]
Therefore, the length of QR is:
[tex]\LARGE\boxed{\boxed{24\; \sf inches}}[/tex]
