Geometry & circle theorems. [question:21]
This is the link to a paper I need help with, only the 21st question. I need to know why they are the sizes they are, for example, I've been taught about the alternate segment theorem but it doesn't apply here? why is this? Link: https://www.mrbartonmaths.com/resources/GCSE%20Revision/Past%20Papers/13.%20June%202014/1hjune2014ans.pdf [question:21]
Original post by WarHammer-
This is the link to a paper I need help with, only the 21st question. I need to know why they are the sizes they are, for example, I've been taught about the alternate segment theorem but it doesn't apply here? why is this? Link: https://www.mrbartonmaths.com/resources/GCSE%20Revision/Past%20Papers/13.%20June%202014/1hjune2014ans.pdf [question:21]
I guess the key is here that if you draw two radii and then a chord between the two point some on the circle, the angle between each radius and the chord is equal (in this case 15) as it forms an isosceles triangle
Why this is, admittedly have no idea. Someone else will know
Edit: I suppose this is because any radi are of equal length, so it's automatically an isosceles triangle
(edited 7 years ago)
Original post by WarHammer-
This is the link to a paper I need help with, only the 21st question. I need to know why they are the sizes they are, for example, I've been taught about the alternate segment theorem but it doesn't apply here? why is this? Link: https://www.mrbartonmaths.com/resources/GCSE%20Revision/Past%20Papers/13.%20June%202014/1hjune2014ans.pdf [question:21]
Angle ABE is 180, so OBC= 180 -90-75 = 15. And sort angles in triangle OBC
ABOD is a quadrilateral, sum of angles 360, so BOD = 360-40-90-90=140
Then for triangle ODC,
either DCB is half DOB = 70, so DCO = 70-15=55, and so does ODC,
or sum of angle round O is 360, so DOC = 360-150-140=70, and ODC = (180-70)/2
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