Triangle ABC is inscribed in a circle as shown in the figure. AX,BY and CZ bisect ∟A,∟BAnd ∟C respectively. If ∟BAC= 56 degrees, ∟ABC=64 degrees. Find the angles of ▲ XYZ. A,Y,C,X,Z in clockwise.
Hello, snigdha!
Thereom: An inscribed angle is measured by one-half its intercepted arc.Triangle is inscribed in a circle as shown in the figure.
bisect , respectively.
If
find the angles of
Since , then: .
Since , then: .
Hence: .
Therefore: .
Since bisects
Since bisects
Hence: .
. . Therefore: .