What special kind of triangle is ABC?Hello, I am stuck on this question where I can find y but don't understand how to find x and z, I am not sure which circle theorem rule to use any help would be appreciated thanks!
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I believe the measure of minor arc CD is the angle (y = 40°) that Ian has already determined (given that he knows it's twice the angle subtended at the circumference by the same arc, I presume; how else would he get that without first finding "z"?).What special kind of triangle is ABC?
What is the measure of (minor) arc CD?
You may be misreading the figure. It is arc AD whose measure is 40°, not CD. Arc CD, which can be found using angle y, is useful for finding angle z.I believe the measure of minor arc CD is the angle (y = 40°) that Ian has already determined (given that he knows it's twice the angle subtended at the circumference by the same arc, I presume; how else would he get that without first finding "z"?).
No, I am not misreading the figure. I simply presumed (wrongly, ofc) that you were referring to minor arc AD (without checking back to the diagram) because that was how he had appeared to have arrived at his answer of 40° for "y" (without first getting "z"). Mea culpa!You may be misreading the figure. It is arc AD whose measure is 40°, not CD. Arc CD, which can be found using angle y, is useful for finding angle z.
Or, of course, you could just use triangle ADC, as pka has pointed out.
Tato is not the OP! We don't yet know whether the OP has learned anything.Your answers are now correct. (Except for missing units! "X=45" is not the same as "X=45°". Mathematics is a language that requires a minimum level of precision.)
Were you asked to calculate the sum of the three angles? I am curious as to why you have done so; it is not pertinent to finding the individual sizes of x, y & z.
The facts (knowledge) you needed to find these angles is summarized below. You appeared to be familiar with point 1 (in the picture) but did not seem to be aware of points 2 & 3 when you came to us for assistance. Several hints were provided to lead you towards these facts and I trust that is how you eventually arrived at your answers?
Indeed! Thank you for pointing that out. I had seen Tato's name crop up elsewhere as both questioner & contributor and just assumed this was his thread.Tato is not the OP! We don't yet know whether the OP has learned anything.
(I make that mistake sometimes, too.)
I thought that y was angle at the centre so i times it by 2 from angle DCA thats how i got 40° Ill tried using the resources you sent me and I think i understand it now thanksNo, I am not misreading the figure. I simply presumed (wrongly, ofc) that you were referring to minor arc AD (without checking back to the diagram) because that was how he had appeared to have arrived at his answer of 40° for "y" (without first getting "z"). Mea culpa!
I will endeavour to check your comments more carefully in future.
Your suggestion does, indeed, lead towards evaluation of angle y and the repeated hints about the angles in a semi-circle also allow for finding not only angle z (as pka suggests) but also angle x, except that he appears to be lacking the knowledge of a basic fact about isosceles triangles that would lead to the final solutions required.
Note to Ian goh: In addition to the website I mentioned already on the Properties of Circles, please also visit this website on the Properties of Triangles. Together, these sites give you all the information you need to solve your problem (and the revision won't do you any harm at all!).
Yes, you now have the correct answers.I thought that y was angle at the centre so i times it by 2 from angle DCA thats how i got 40° Ill tried using the resources you sent me and I think i understand it now thanks