Circle Theorems Explained | Maths GCSE

A quick example of solving a circle theorem question to help with your maths GCSE revision!
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[@revisionboost]

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[@rykercordova5016]

I have a state test in a bit, just refreshing my head before it so I can do my best on it.

[@ConstantDerivative]

I think you can use the "center angle is double the angle at the circumference" theorem first, getting 240 degrees, and then doing 360-240?

[@ggmania4647]

Yes

[@henry_3300]

the theorem youre referring to actually states that an inscribed angle's measure, which is what given angle 120° is, is half the length of the degree measure of the arc it intercepts (called Inscribed Angle Theorem). in this case, since we are given the angle measure, we can simply double it to find the degree measure of the arc intercepted by the inscribed angle.
lastly, to find the central angle x, we must first understand that the arc that a central angle intercepts has equal degree measures as the central angle itself. in this case, to figure out the rest of the circle's arc, we simply subtract 240 from 360, yielding the result of 120°.

[@Kaur370]

The sum of opposite angle in quadrilateral circumscribe a circle is 180. So 120+x=180 x =60. Therefore Centre at angle is double = 60 into 2 = 120

[@apsingh1792]

You are the best teacher thank you 😊 ❤

[@WillieChiwaya-zw2bl]

Thank you your good teacher

[@kirki221]

I did it kind of different, I said that because angles at the centre of a circle are 2x the size of angles at the circumference, the reflex of x has to be 240 than you subtract that from 360 to get x

[@asilbekqurbonov5168]

thank you, bro

[@mirettekengne2744]

math gives énergy😤🔌

[@preetisharma-bj5yc]

did it in my head 😅

[@arnav1689]

very helpful

[@conradm7244]

The thing that confuses me is isnt the 120 also on the edge why don't we times that by 2

[@memerboy727]

Thanks bro

[@revisionboost]

Welcome!

[@ts-mq6ve]

g i in yr 10 an never seen that in my life

[@karticksantra770]

As an indian i really solved it within 1 second

[@_ftav8]

Couldn't we say x=120 (angles on opposite sides)?

[@icecream-sv6vc]

naah noo we can't we just can't

[@_ftav8]

@@icecream-sv6vc could i know the reason for that?

[@icecream-sv6vc]

​@@_ftav8 because there is no "angles on opposite sides" theorem for a quadrilateral like the one formed here. if we say that the angle given 120 is y, an equation for this question is (180-y)*2=x, and a value of x was chosen equal to y, which is 120. But, x doesn't need to be equal to y.

[@_ftav8]

@@icecream-sv6vc Thank you very much. I appreciate it 🙏🏻🙏🏻

[@fakesmile2643]

smartest unasian 🗿

[@spartanclipjya]

I solved this in like 1 seconds lmao

[@ElPaume1]

The angle from the center and the 120 is related which therefore means:
ô = 240° (< at center=2x < at the circumference)

[@mbalikellydube9265]

No that's not a cyclic quad

[@freedwolves582]

Let’s ignore the fact that all quadrilaterals add up to 360 degrees

[@im.rishabh_ofc]

U need to, for this question

[@ConstantDerivative]

it does, but theres an extra rule for cyclic quadrilaterals

[@user-no6hd7wd4t]

Wrong theorem sir X will be 30

[@Grizzly01-vr4pn]

Oh dear. Back to revision for you.

[@ENDO125RAPTER]

I'm pretty sure X is 90 degrees

[@Little_Bubbly]

not quite, if it was 90 then there would be a square there to show that it’s a right angle

[@Emanali55559x]

No

[@Grizzly01-vr4pn]

Show your working...
Or are you saying that it _looks_ like it should be 90°, when we all should know that such geometry diagrams should never be assumed to be to scale unless they state that they are?

[@ENDO125RAPTER]

y'all do know i'm being sarcastic, right?

[@Grizzly01-vr4pn]

@@ENDO125RAPTER Convenient.