MathDB

p25. Compute:

\frac{ \sum^{\infty}_{i=0}\frac{(2\pi)^{4i+1}}{(4i+1)!}}{\sum^{\infty}_{i=0}\frac{(2\pi)^{4i+1}}{(4i+3)!}}

p26. Suppose points

A, B, C, D

lie on a circle

\omega

with radius

4

such that

ABCD

is a quadrilateral with

AB = 6

AC = 8

AD = 7

. Let

E

and

F

be points on

\omega

such that

AE

and

AF

are respectively the angle bisectors of

\angle BAC

and

\angle DAC

. Compute the area of quadrilateral

AECF

.
p27. Let

P(x) = x^2 - ax + 8

with a a positive integer, and suppose that

P

has two distinct real roots

r

and

s

. Points

(r, 0)

(0, s)

, and

(t, t)

for some positive integer t are selected on the coordinate plane to form a triangle with an area of

2021

. Determine the minimum possible value of

a + t

.
p28. A quartic

p(x)

has a double root at

x = -\frac{21}{4}

, and

p(x) - 1344x

has two double roots each

\frac14

less than an integer. What are these two double roots?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

R7

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