Recap activity #16 with the Circle Theorems on one page.
** Answers included in the PowerPoint file **
(Prompted by original pile-up ideas from others on Pythagoras, Trigonometry - and Circle Theorems.)
This puzzle is the sixteenth in a series of consolidation exercises/angle chases on the topic of Circle Theorems.
All of the Circle Theorems are present with “two radii and a chord make an isosceles triangle” and “a radius that is perpendicular to a chord divides the chord into two equal parts” in there too.
**NB - this exercise has been created to encourage students to add their own lines in order to find some of the answers. Amended March 2020 without changing any of the answers **
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Great resource...except I can't get past finding c!! So challenging. Any help?
keyboardmonkey
8 months ago
I think by now you will have picked up the answer elsewhere, but start by using the angle fact that 'two radii form an isosceles triangle' then add a couple of chords from the points on the circumference where the known angles are given. Then use the Circle Theorem 'the angle in a semi-circle is a right angle' (twice). To get 'c' you will need to use 'opposite angles in a cyclic quadrilateral'. Thanks for the five star rating :)
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Great resource. As I worked through this one, should the 9 degrees point to the top right angle instead of the bottom right? That way you can use angle at centre is twice angle at circumference. I can't seem to get it to work to give your answers otherwise.
keyboardmonkey
a year ago
Thank you very much for the five star review. Much appreciated as this is one of the resources I most enjoyed creating.
As far as the 9 degrees is concerned I show that figure as you need to add 18 + 3d + 88 + 2g = 360 degrees. I've printed off and completed the full sheet from scratch - crikey, how did I find the time back then? - and I get it all to tally. Have another look, perhaps?
Thanks again for the review - KM.
Empty reply does not make any sense for the end user
