Question

高中几何问题求解

Answer 1

(1)Obviously：阿尔巴=arctan(1/q),
Obviously,三角形AEG∽三角形CHF,（because 角DCA=角DAC and 角AEG=角CHF）

and,角HFC=角AGE=贝塔=arctan(1/q);
(2)Obviously tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)=tan(180度-45度)
and -1=(1/p+1/q)/(1-1/q*1/p)
-1=(p+q)/(pq-1)
p+q=1-pq
(3)because p+q=1-pq,
and q=(1-p)/(1+p)
S（BEDF）=ABCD-ABE-BCF
=1-1/2p-1/2q
=1-1/2p-1/2(1-p)/(1+p)
=1-1/2p+(p-1)/(2(1+p))
(4)Obviously 0<p<=1
S（BEDF）=1-1/2p+(p-1)/(2(1+p))
=1+（-p(1+p)+p-1）/(2(1+p))
=1+(-p^2-1)/(2(1+p))
when p=1,max=1/2
做完这道题，我感觉到智商受到了。。。