MathDB

i.) Let

ABC

be a triangle with

AB = 12

and

AC = 16.

Suppose

M

is the midpoint of side

BC

and points

E

and

F

are chosen on sides

AC

and

AB

, respectively, and suppose that lines

EF

and

AM

intersect at

G.

AE = 2 \cdot AF

then find the ratio

\frac{EG}{GF}

ii.) Let

E

be a point external to a circle and suppose that two chords

EAB

and

EDC

meet at angle of

40^{\circ}.

AB = BC = CD

find the size of angle

ACD.

Problem Statement