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The point P in the trapezium ABCD

Source: CentroAmerican 2004

December 10, 2010

geometrytrapezoidcircumcircleangle bisectorgeometry proposed

Problem Statement

Let

ABCD

be a trapezium such that

AB||CD

and

AB+CD=AD

. Let

P

be the point on

AD

such that

AP=AB

and

PD=CD

.

a)

Prove that

\angle BPC=90^{\circ}

.

b)

Q

is the midpoint of

BC

and

R

is the point of intersection between the line

AD

and the circle passing through the points

B,A

and

Q

. Show that the points

B,P,R

and

C

are concyclic.

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