Question 10
A circle with centre $O$ has diameter $AD$. With $X$ on $AO$ and points $B$ and $C$ on the circle, triangles $ABX$ and $XCO$ are similar isosceles with base angles $\alpha$ as shown. Find, with proof, the value of $\alpha$.
Investigation (separate manual bonus, not part of the 5 base marks). The $1+2=3$ bonus marks are assessed manually and separately from the contest base total of 35.
(a) Find $\alpha$ if, instead of two similar isosceles triangles on $AO$, there are three. [1 bonus mark]
(b) Find $\alpha$ if there are $n$ similar isosceles triangles along $AO$. [2 bonus marks]
Investigation (separate manual bonus, not part of the 5 base marks). The $1+2=3$ bonus marks are assessed manually and separately from the contest base total of 35.
(a) Find $\alpha$ if, instead of two similar isosceles triangles on $AO$, there are three. [1 bonus mark]
(b) Find $\alpha$ if there are $n$ similar isosceles triangles along $AO$. [2 bonus marks]