O is the center of the semicircle, if angle EOD=45^circ and OD = AB, find angle BAC

makeupwn

makeupwn

Answered question

2022-08-13

How to find an angle between the extension of a diameter and a chord in a semicircle

O is the center of the semicircle, if E O D = 45 and O D = A B, find B A C

Answer & Explanation

Brooks Hogan

Brooks Hogan

Beginner2022-08-14Added 18 answers

Step 1
Let B A C = α.
A B O is isosceles with B A O = A O B = α and A B O = 180 2 α.
O B E = 180 A B O = 2 α
B O E is isosceles with O B E = B E O = 2 α and B O E = 180 4 α.
Step 2
Now you have A O B + B O E + E O D = 180
α + ( 180 4 α ) + 45 = 180
α = 15

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