ray ac is tangent to circle O at A. If the measure of arc BY=24, what is mof angle YAC? (The figure is not drawn to scale.) A. 132 B. 48 C. 78 D. 156

Question

anonymous · Answer

https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_12_files/mc010-4.jpg

ganeshie8 · Answer

since AC is tangent, angle BAC = 90

ganeshie8 · Answer

but question is asking for angle YAC :
YAC = BAC - BAY
       = 90 - BAY

ganeshie8 · Answer

any ideas how to find angle BAY ?

anonymous · Answer

okay how would I find it im not exactly sure

ganeshie8 · Answer

we are given BY = 24, that means, central angel BOY = 24

ganeshie8 · Answer

still we are looking for BAY, not BOY right

anonymous · Answer

i believe so

ganeshie8 · Answer

BOY is called central angle
BAY is called inscribed angle

and we have a relation between these two :
inscribed angel = central angle/2

so BAY = ?

anonymous · Answer

bay=24^2  ?

ganeshie8 · Answer

u mean 24/2 ?

anonymous · Answer

yeah so it would be 24 divide 2 right to get the answer

ganeshie8 · Answer

BAY = 24/2 = 12

anonymous · Answer

okay im understanding it better lol

ganeshie8 · Answer

plug BAY in the equation given above

ganeshie8 · Answer

YAC = BAC - BAY
       = 90 - BAY
       = 90 - 12
       = ?

anonymous · Answer

78 ? am i right

ganeshie8 · Answer

^right

anonymous · Answer

thank you again :)

ganeshie8 · Answer

yw !