Question

Let P be the midpoint of HM. Line segments MT and AP intersect at point Q. The radius of the largest circle contained in quadrilateral QTHP can be written in the form
`a-√(b)`, where a, b are positive integers such that b is square-free. What is the value of
`a+b`?

Answer 1

To find the radius of the largest circle contained in quadrilateral QTHP, use the properties of midpoints and intersecting line segments.

Step-by-step explanation:

To find the radius of the largest circle contained in quadrilateral QTHP, we can use the properties of midpoints and intersecting line segments. Since P is the midpoint of HM, we can use the Midpoint Formula to find the coordinates of P. Then, we can find the coordinates of the point of intersection, Q, by solving for the intersection of line segments MT and AP using the equations of their lines. Once we have the coordinates of Q, we can use the Distance Formula to find the length of QT. Finally, the radius of the largest circle contained in quadrilateral QTHP will be half the length of QT.