中四 math!

15a) radius=OB
AP perpendicular to BC
BP=PC=16/2=8cm
OP=6cm
By Pyth. theorem,
OB^2=OP^2 + PB^2
=6^2+8^2
=36+64
=100
OB=10
radius=10cm

15b) OA is radius,thus OA=10cm(from a)
OP=6cm
AP=10+6
=16cm
By Pyth. theorem,
AB^2=PB^2 + AP^2
=8^2 + 16^2
=320
AB=17.9cm(3 sig. fig.)

16a) Let OM=y cm
OD=OB=radius=(y+2) cm(因為OB=y+2)
By Pyth. theorem,
(y+2)^2 = y^2 + 4^2
y^2+4y+4= y^2 + 16
y^2+4y+4-y^2=16
4y+4=16
4y=12
y=3
since OB is the radius
Thus, OB=y+2
=3+2
=5cm

16b) From a, ON=OM=y=3cm

15) a) r = (6^2 + 8^2)^0.5 = 10
b) ((AO + OP)^2 + PC^2)^0.5 = ((10+6)^2 + 8^2)^0.5 = 17.XXX

16)a) (R-2)^2 + 4^2 = R^2
R=5
b) ON=5-2 = 3