MathDB

2014-2015 Spring OMO #17

Source:

April 14, 2015

Online Math Open

Problem Statement

Let

A,B,M,C,D

be distinct points on a line such that

AB=BM=MC=CD=6.

Circles

\omega_1

and

\omega_2

with centers

O_1

and

O_2

and radius

4

and

9

are tangent to line

AD

at

A

and

D

respectively such that

O_1,O_2

lie on the same side of line

AD.

Let

P

be the point such that

PB\perp O_1M

and

PC\perp O_2M.

Determine the value of

PO_2^2-PO_1^2.

Proposed by Ray Li

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