MathDB

(1)

D

is an arbitary point in

\triangle{ABC}

. Prove that:

\frac{BC}{\min{AD,BD,CD}} \geq \{ \begin{array}{c} \displaystyle 2\sin{A}, \ \angle{A}< 90^o \\ \\ 2, \ \angle{A} \geq 90^o \end{array}

(2)

E

is an arbitary point in convex quadrilateral

ABCD

. Denote

k

the ratio of the largest and least distances of any two points among

A

B

C

D

E

. Prove that

k \geq 2\sin{70^o}

. Can equality be achieved?

Problem Statement