Soal Olimpiade (MBI PPPPTK Matematika)

1. Find the value of n given that (10²⁰¹⁰ + 25)² – (10²⁰¹⁰ – 25)² = 10ⁿ. [Score 3].
2. An equilateral triangle is inscribed in a circle. Points M and N are the mid-points of AB and AC respectively. Line segment MN is extended to meet the circumference at P. Find the ratio of MN : NP. [Score 4]
3.  Steve is planning a cross-country run for his club. He plans a course, starting at O, that follows the arrows from O to A, around the arc APB which is part of a circle which can be represented by the equation (x – 12)² + (y – 5)² = 25 then from B back to the starting point O. OA and OB are tangents to the circle. What is the total length of the run. (All distances are in km). [Score 5]