Question

Line XY bisects and is perpendicular to AB and CD. CD = 10 and XY = 24. What is the length of AP?

Answer 1

AP = 13

Explanation:

See the attached figure.

CD = 10 and XY = 24

Line XY bisects and is perpendicular to AB and CD

∴ XY bisects at Y

∴ CY = 0.5 CD = 0.5 * 10 = 5

And from the geometry of the shape

P is the midpoint of XY

∴ XP = YP = 0.5 XY = 0.5 * 24 = 12

XY is perpendicular to CD

∴ ΔPYC is a right triangle at Y

∴ PC (hypotenuse) =
`√(PY^2+YC^2) =√(12^2+5^2)=√(144+25) =√(169) =13`

From the figure AP = PC = 13