ｍａｔｈｓ　ｆ．４ 10 pts

1
a ) find x and y
b) find angle BCQ
c} find arc AD : arc DC
a)
angle ABR=180-88-32=60
angle CBD=angle CAD=x
consider triangle ABP
48+x+32+60+x=180
x=20
angle ABC=60+20=80
angle ADC=180-80=100
consider triangle ADQ
32+20+100+y=180
y=28
b)
angle BCD=180-20-32=148
angle BCQ=180-148=42
c)
arc AD : arc DC
=angle ABD: angle CAD
=80:20
=4:1
2 ) arc BC = arc DE , AD prependicular to BF,
FP = 8 cm,PQ = 6cm and AS = 16 cm .
a ) Show that P , Q , R and S are concylic
a)
angle PQR=90
angle DAE=angle BFC
angle ARF=angle ARF
so 180-angle DAE-angle ARF=180- angle BFC-angle ARF
angle ASR=angle PQR=90
Now angle ASR+angle PQR=90+90=180
So P , Q , R and S are concylic