In `DeltaAEX, T` is the midpoint of XE and P is the midpoint of ET. If `DeltaAPE` is equilateral of side length equal to unity, then the vaue of `(AX)^(2)` is _____

Answer

13

Explanation

We have `AE = EP = AP =1`
`rArr AP = PT = 1`
Hence, `DeltaAPT` is isosceles
`rArr angleEAT = 90^(@)`
Hence, `AT = sqrt3`. Now, `angleATX = 150^(@)`

Since TX = 2, by applying the cosine rule in `DeltaATX`, we get
`(AX)^(2) = 3 + 4 - 4 sqrt3 cos 150^(@) = 7 + 6 = 13`