MathDB

15

Part of 2022 AMC 10

Problems(2)

2022 AMC 10 A Problem 15

Source: 2022 AMC 10A #15

11/11/2022
Quadrilateral ABCDABCD with side lengths AB=7,BC=24,CD=20,DA=15AB=7, BC = 24, CD = 20, DA = 15 is inscribed in a circle. The area interior to the circle but exterior to the quadrilateral can be written in the form aπ−bc\frac{a\pi - b}{c}, where a,b,a, b, and cc are positive integers such that aa and cc have no common prime factor. What is a+b+ca+b+c?
<spanclass=′latex−bold′>(A)</span>260<spanclass=′latex−bold′>(B)</span>855<spanclass=′latex−bold′>(C)</span>1235<spanclass=′latex−bold′>(D)</span>1565<spanclass=′latex−bold′>(E)</span>1997<span class='latex-bold'>(A) </span> 260 \qquad <span class='latex-bold'>(B) </span> 855 \qquad <span class='latex-bold'>(C) </span> 1235 \qquad <span class='latex-bold'>(D) </span> 1565 \qquad <span class='latex-bold'>(E) </span> 1997
AMC 10AMCgeometrycyclic quadrilateral2022 AMC 10a2022 AMC
Ratio of Sums of an Arithmetic Sequence

Source: 2022 AMC 10B #15

11/17/2022
Let SnS_n be the sum of the first nn term of an arithmetic sequence that has a common difference of 22. The quotient S3nSn\frac{S_{3n}}{S_n} does not depend on nn. What is S20S_{20}?
<spanclass=′latex−bold′>(A)</span>340<spanclass=′latex−bold′>(B)</span>360<spanclass=′latex−bold′>(C)</span>380<spanclass=′latex−bold′>(D)</span>400<spanclass=′latex−bold′>(E)</span>420<span class='latex-bold'>(A) </span> 340 \qquad <span class='latex-bold'>(B) </span> 360 \qquad <span class='latex-bold'>(C) </span> 380 \qquad <span class='latex-bold'>(D) </span> 400 \qquad <span class='latex-bold'>(E) </span> 420
ratioarithmetic sequence