Finding circumcenter

80 Views Asked by At

In a triangle A(1,2) B(2,3) C(3,1) and $\angle A = cos^{-1}(4/5)$, $\angle B = \angle C = cos^{-1}(\frac{1}{\sqrt{10} }) $
Ordinate of circumcentre of the $\triangle$ is ?

I have tried solving by finding the equation for line perpendicular to AC and BC and then finding the intersection point. The ordinate I found was 11/3, but the answer provided is 0. Can anyone pls solve this using the angles provided, and also tell me whether my method is correct or not? Thanks.

1

There are 1 best solutions below

2
On BEST ANSWER

Your method is correct but the calculation may be off because it is $\frac{11}{6}$ . There is no way it can be $0$ though.

The angles were probably given because the circumcentre's Y co-ordinate can also be expressed as:

$$Y_c=\frac{y_1sin2A+y_2sin2B+y_3sin2C}{sin2A+sin2B+sin2C}$$

Where $y_1,y_2,y_3$ are the ordinates of the vertices and A,B,C are the angles at those vertices.