Online Course Discussion Forum

Geometry II-A

Picture of Virginia Zhu
Geometry II-A
by Virginia Zhu - Wednesday, August 17, 2022, 10:57 PM

Hey, is it possible to provide a solution for problem 7.28 a)  and b)? I've been stuck for a long time

Picture of John Lensmire
Re: Geometry II-A
by John Lensmire - Thursday, August 18, 2022, 9:55 AM

Let me give a diagram and some hints that should help.

To get started for (a), what special triangles are ACE and BDE? Then, the key idea to remember: "The perpendicular bisector of any chord goes through the center of the circle". Hence, it we draw the perpendicular bisectors from midpoints M (of AB) and N (of CD) they intersect at the center of the circle O. Noting that EOM and EON are also special triangles should make part (a) fairly easy to finish from here.

Part (b) should be pretty easy from this setup / diagram. Hint: AO is a radius.

Hope this helps! I'm happy to add more details, but it is good practice to try filling in the details first!