Question

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?​

Answer 1

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