MathDB

BMT 2021 Geometry #5

Source:

August 12, 2023

geometry

Problem Statement

Let circles

\omega_1

and

\omega_2

intersect at

P

and

Q

. Let the line externally tangent to both circles that is closer to

Q

touch

\omega_1

at

A

and

\omega_2

at

B

. Let point

T

lie on segment

P Q

such that

\angle AT B = 90^o

. Given that

AT = 6

,

BT = 8

, and

P T = 4

, compute

P Q

.

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