Can someone help me with this circle geo Question (1 Viewer)

[StudyMaster101]

Yeah i'm a bit lost.

Its from cambridge yr 11 3u, Exercise 14H Q18

I think you use A=1/2 (absinC)



Thanks.

 

[Drongoski]

Yeah i'm a bit lost.

Its from cambridge yr 11 3u, Exercise 14H Q18

I think you use A=1/2 (absinC)

View attachment 34563

Thanks.

Since PSQ is right-angled at S, PS = d cos @

Using: Area of triangle A = "(1/2)absinC" = (1/2) dcos@ x dcos @ x sin @ = (1/2)d²cos²@sin @

dA/d@ = 0.5d²cos@(1-3sin²@) = 0 when A is maximum.

Solving: sin²@ = 1/3

Substitute this into A = 0.5d²(1 - sin²@)sin@
you get A-max = the reqd result.