In triangle ABC, AB = 8, AC = 3, and the altitude from A to BC is 2. What is the radius of the circle passing through, A, B and C?
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Answer:
In triangle AOB,
AB
2
=AO
2
+OB
2
(Pythagoras theorem)
AO
2
=AB
2
−OB
2
(I)
In triangle AOC,
AC
2
=OC
2
+AO
2
(Pythagoras theorem)
AO
2
=AC
2
−OC
2
(II)
From I and II,
AB
2
−OB
2
=AC
2
−OC
2
AB
2
−(OC+BC)
2
=AC
2
−OC
2
8
2
−(OC+6)
2
=3
2
−OC
2
64−OC
2
−36−12OC=9−OC
2
12OC=19
OC=
12
19
= 1
12
7
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