Find M<BAC . .. . .

Question

Given: Circle O, r =3, AB = 2, AC = 4

O ∈ exterior of ∠BAC Find m∠BAC

Answer 1

Let draw diameer AD = 2r = 6. ΔABD with right angle ∠B: so, cos(∠BAD) = 2/6 = 1/3

ΔACD with right angle ∠C, cos(∠CAD) = 4/6 = 2/3 ;

∠BAC = ∠BAD - ∠CAD) = cos^-1(1/3) - cos^-1(2/3) = 22.34°

Answer 2

Draw the radii to A and B

Use the law of cosines in ΔAOC to get the angle between the radius OA and AC...call it angle x

Then use the law of cosines in triangle AOB to get angle BAO.

Subtract angle x from angle BAO to get angle BAC