YLL討論網

在半徑為r的一個圓,弦(chord)AB的長度是10,弦CD的長度是7,
過B點延長AB,過點C延長DC,相交於圓外一點P.
angleAPD=60degree,BP=8,r=?

Let PC=a
By intersecting chord theorem,
a/18=8/(a+7)
a^2+7a-144=0
(a+16)(a-9)=0
a=9
PC=9

Let O be the center
Extend AO, let it intersects the circle at E.
angle ABE=90(angle in semi-circle)
BE=8tan60=8sqrt3

AE^2 = 10^2+(8sqrt3)^2
=100+192
=292
AE=2sqrt73

r=sqrt73

Let O be the center
Extend AO, let it intersects the circle at E.
angle ABE=90(angle in semi-circle)
BE=8tan60=8sqrt3

You have not proved that D and E are the same point

Don't have to be same point, D is useless