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A level radians question

hey guys1 I'm really stuck on part b of this question so can anyone help?

A circle with centre O and radius 8cm passes through points A and B such that OAB is an equilateral triangle. the point P is on the major arc AB. Find, in terms of pi,
(a) the size of the angle APB,
(b) the perimeter of the major segment ABP.


for (a) I got pi/6 radians and for part b I just cant thing of what equations I need to use and how it would work for the circle
Original post by khadijahammad33
hey guys1 I'm really stuck on part b of this question so can anyone help?

A circle with centre O and radius 8cm passes through points A and B such that OAB is an equilateral triangle. the point P is on the major arc AB. Find, in terms of pi,
(a) the size of the angle APB,
(b) the perimeter of the major segment ABP.


for (a) I got pi/6 radians and for part b I just cant thing of what equations I need to use and how it would work for the circle


Just ignore this post - brain fart!
(edited 4 years ago)
Reply 2
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Untitled.png I think this is how she approached the first part.
Original post by ghostwalker
Part (a) is incorrect. P lies on the major arc, not the minor arc.

Part (b), Perimeter is simply the sum of the radii and the arc length. And when θ\theta is in radians, the arc length, s, is given by s=rθs=r\theta
Original post by : ).
Untitled.png I think this is how she approached the first part.


Makes sense.

I was thinking of the angle subtended by the major arc. Misinterpreted.
Original post by ghostwalker
Part (a) - Fine (Edit: corrected - see : ). below.)

Part (b), Perimeter is simply the sum of the radii and the arc length. And when θ\theta is in radians, the arc length, s, is given by s=rθs=r\theta


could you possibly show a diagram of what the major segment ABP is as im still unsure about which part it literally is - like outline it? that would help so much
yep that's how I did it : )
Original post by : ).
Untitled.png I think this is how she approached the first part.
Original post by khadijahammad33
could you possibly show a diagram of what the major segment ABP is as im still unsure about which part it literally is - like outline it? that would help so much


Ignore what I said previously. For some reason I was thinking of sectors rather than segments.

I would interpret part (b) to refer the the area in the attached diagram (part cribbed from : ). - ta!)

Untitled.png
Reply 7
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bwahaha...cute!! .

perimeter = arc length (AB major segment) + 8
Original post by ghostwalker
Just ignore this most - brain fart!
thanks very much
Original post by ghostwalker
Ignore what I said previously. For some reason I was thinking of sectors rather than segments.

I would interpret part (b) to refer the the area in the attached diagram (part cribbed from : ). - ta!)

Untitled.png
oh is the length of AB (chord) 8?
Original post by : ).
bwahaha...cute!! .

perimeter = arc length (AB major segment) + 8
Reply 10
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..the radius of the circle is 8cm...and it is an equilateral triangle
,,.png
Original post by khadijahammad33
oh is the length of AB (chord) 8?
right yeah thanks idk why I even asked that q
Original post by : ).
..the radius of the circle is 8cm...and it is an equilateral triangle
,,.png

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