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In ▲XYZ, ∠X = 52° and ∠Y = 57°. One circle passes through Y, Z, and...

In ▲XYZ, ∠X = 52° and ∠Y = 57°. One circle passes through Y, Z, and the incenter of ▲XYZ, and a second circle passes through X, Z, and the circumcenter of ▲XYZ. What is the degree measure of the acute angle the two circles intersect at?

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Answer #1

The bothe circles intersect the XYZ through the vertex Z and the side XY

We can see that the line ZE divides the XYZ as two right angle triangle and

180-52-90 and   180-57-90

(Total angle of any triangle is 180 degree)

38 degree

33 degree

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