Geometry Book Hard Practice Q.9

[domivantman]

Question 9 Geometry,
I don't know why I can't upload a photo, but here's the link for the picture: https://drive.google.com/file/d/0B6bKRx ... sp=sharing

Why in the answer they assume that segment AC passes through the center of the circle? Because for that reason they assume that angles CAD and ACB are both inscribed angles of the circle?

Thanks

[tommywallach]

Hey Domivant

Actually, the question does not assume it passes through the center. (The explanation doesn't say that at all.) I would recommend you read it more closely. Draw the line from B to D. You know that ADB is also 45 (because the lines are parallel).

Now, any angle PULLED from the edge of a circle TO the center doubles. So if you PULL point A from where it is to the center (again, not assuming AC is a diameter, which it isn't), that angle would now be 90. This is just a rule. It is NOW a central angle. Similarly, point D, when pulled to the center, would become 90. So now the two arcs (from A to B and from C to D) take up 180 degrees. That leaves 180 degrees for BXC and AYD.

From there, all you do is solve for the circumference, divide it into thirds, and assign one third to BXC (because the other two-thirds) belong to AYD. Hope that makes sense!

-t