Circle in the Corner

A regular hexagon ABCDEF has the side length of 6. Circle O is inscribed in the hexagon. The tangent points on AB and AF are G and H respectively. Circle P is inscribed in the corner area sounded by HA, AG, and arc GH. What's the radius of circle P? (Do not use calculator. Let the square root of 3 be 1.73. When submitting the result, keep two digits after decimal point.)

Triangles in a Grid

Nine dots form a 3 by 3 grid. The distance between any two adjacent dots in the left-right or up-down direction is the same. How many triangles can be formed from this grid by choosing three dots as the vertices?

Meetup in Classroom

Dr. Hong decides to gather the CMM students for a face-to-face meetup in a classroom, where 90 seats are arranged in a 9 by 10 grid. The distance between two adjacent seats in any row or column is 5 feet. Due to the concern of COVID-19, Dr. Hong wants to keep at least 6 feet distance between any two students. What's the maximum number of students Dr. Hong could bring to the classroom?