MathDB

As shown in the figure, it is known that the quadrilateral

ABCD

satisfies

\angle ADB = \angle ACB = 90^o

. Suppose

AC

and

BD

intersect at point

P

, point

R

lies on

CD

and

RP \perp AB

M

and

N

are the midpoints of

AB

and

CD

respectively. Point

K

is a point on the extension line of

NM

, the circumscribed circles of

\vartriangle DKC

and

\vartriangle AKB

intersect at point

S

. Prove that

KS \perp SR

. https://cdn.artofproblemsolving.com/attachments/5/d/fc0a391f8ebcdee792e9b226cbf55a058251a1.png

Problem 1