Coodinate geo question!! CIE

Hello, I don't get the first part of this question, it tells you the area of the triangle and the segment are equal.
https://gyazo.com/c18d05c07dbdfba700e1eee58affc014

So i guess:

Area of triangle:
0.5*a*b*sinc
0.5*r*r*sinθ
0.5*r^2sinθ

Then segment is sector area - triangle so:
(0.5r^2θ) - (0.5*r^2sinθ)

And are of triangle = segment so:
0.5*r^2sinθ = (0.5r^2θ) - (0.5*r^2sinθ)

But I don't get how or where would the P come from.

Is my working out up till now correct? Or have I misread the question.

Hello, I don't get the first part of this question, it tells you the area of the triangle and the segment are equal.
https://gyazo.com/c18d05c07dbdfba700e1eee58affc014

So i guess:

Area of triangle:
0.5*a*b*sinc
0.5*r*r*sinθ
0.5*r^2sinθ

Then segment is sector area - triangle so:
(0.5r^2θ) - (0.5*r^2sinθ)

And are of triangle = segment so:
0.5*r^2sinθ = (0.5r^2θ) - (0.5*r^2sinθ)

But I don't get how or where would the P come from.

Is my working out up till now correct? Or have I misread the question.

how do I finish this( if it's right)

So, $\theta = 2 \sin\theta$

Compare this with $\theta = p\sin\theta$

So, p=2

Looks good, the question wants you to find p so mention the value of p.

Also, just for future reference, you could also say:

(Area of traiangle) = (1/2)(Area of sector).

Therefore:

$(1/2)r(r \sin(\theta)) = (1/2) \left[ (1/2) \theta r^{2} \right].$

Simplifying to:

$(1/2) r^{2} \sin(\theta) = (1/4) r^{2} \theta$.

Does that can be used in all cases?

Is it always area of triangle = 0.5*area of sector?

Not sure about it