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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 3
2022 Nigerian MO round 3
Problem 4
Problem 4
Part of
2022 Nigerian MO round 3
Problems
(1)
Two tangents and bisection
Source: 2022 Nigeria MO Round 3/Problem 4
4/17/2022
Let
P
T
PT
PT
and
P
B
PB
PB
be two tangents to a circle,
T
T
T
and
B
B
B
on the circle.
A
B
AB
A
B
is the diameter of the circle through
B
B
B
and
T
H
TH
T
H
is the perpendicular from
T
T
T
to
A
B
AB
A
B
,
H
H
H
on
A
B
AB
A
B
. Prove that
A
P
AP
A
P
bisects
T
H
TH
T
H
.
geometry
Nigeria MO