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Answer:
1) 5.25
2) 95.74°
Step-by-step explanation:
1) The angle bisector divides the triangle into proportional segments.
DC/BD = CA/BA
We know that BD+DC = 9, so we can fill in the above equation with known values to get ...
DC/(9-DC) = 7/5
5·DC = 7(9 -DC) . . . . cross multiply
12·DC = 63 . . . . . add 7·DC
DC = 63/12 = 5.25
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2) Angle BAC can be found using the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (7² +5² -9²)/(2·7·5) = -7/(70) = -1/10
A = arccos(-1/10) ≈ 95.739°
The measure of ∠BAC is about 95.74°.
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Additional comment
The circumcircle is irrelevant to the questions asked here.
