4

Problems(2)

Do u know DA? *click click*

Source: 2018 AIME I #4

3/7/2018

\triangle ABC, AB = AC = 10

and

BC = 12

. Point

D

lies strictly between

A

and

B

\overline{AB}

and point

E

lies strictly between

A

and

C

\overline{AC}

so that

AD = DE = EC

. Then

AD

can be expressed in the form

\tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p + q

AMCAIMEAIME I

Rearranging Names: Caroline is Cornelia

Source: 2018 AIME II #4

3/23/2018

In equiangular octagon

CAROLINE

CA = RO = LI = NE = \sqrt{2}

and

AR = OL = IN = EC = 1

. The self-intersecting octagon

CORNELIA

encloses six non-overlapping triangular regions. Let

K

be the area enclosed by

CORNELIA

, that is, that total area of the six triangular regions. Then

K=\tfrac{a}{b}

where

a

and

b

are relatively prime positive integers. Find

a + b

AMCAIMEAIME II