32. As shown in the figure, the side length of square ABCD is a, take AB as the diameter, make semicircle o, cross point C, make the tangent of semicircle ad to F, and the tangent point is e (1) Verification: OC ⊥ of; (2) Find the perimeter and area of RT △ DCF

32. As shown in the figure, the side length of square ABCD is a, take AB as the diameter, make semicircle o, cross point C, make the tangent of semicircle ad to F, and the tangent point is e (1) Verification: OC ⊥ of; (2) Find the perimeter and area of RT △ DCF

Connect OE
There are
Right triangle CEO and CBO congruence
Aof and EOF congruence of right triangle
Angle AOF = angle EOF
Angle COE = angle BOC
therefore
Angle COF = angle EOF + angle COE = 180 degrees / 2 = 90 degrees
OC⊥OF
2. In right triangle BOC
OC = root (a * a + 0.5A * 0.5A)
=A * radical 1.25
EC = root (1.25A ^ 2-0.25a ^ 2)
=a
Tan angle FCO = 0.5a/a = 0.5 = Tan angle foe
So: Fe = AF = 1 / 2 * OE = 0.25A
FD=a-0.25a=0.75a
The perimeter of RT △ DCF = a + 0.75a + 0.25A + a = 3A
Area = 1 / 2 * a * 0.75a = 0.375a ^ 2