Preparing for the Regents Examination Geometry, AK

8. mHCT 1 _ m
2 TH
mCHT 1 _ CT
2 m
9. mHCT mCHT
10. CTO HTC
11. CT _
CH
TO
_
TH (Corresponding
sides of similar
triangles are in
proportion.)
6 1. Circle O with diameter −−−−
DOG ; DR GI
2. mTEG 1 _ m (
2 DR TG )
3. mTRI 1 _ m (
2 GI TG )
4. TG GI TGI
5. mTEG 1 _ m
2 TGI
6. mTRI 1 _ m
2 TGI
7. mTEG mTRI
8. mRTI mRTI
9. TEX TRI
10.
(AA)
TX _
EX
TI _
RI
11. TX RI EX TI (The product of
means equals
the product of
extremes.)
7 1. CT CH
2. −−−
HA −−
TD
3. CTD CHA; TDH HAT
4. TDH is supplementary to TDC;
HAT is supplementary to HAC.
5. TDC HAC
6. TDC HAC
7.
(AAS AAS)
−−
CT −−−
CH (CPCTC)
8. HA TD
8 1.
(Contradiction)
−−
BC −−−
QR
2. −−
BA −−
QP
3. BC RQ
4. BA QP
(Congruent chords
subtend congruent
arcs.)
5. A D
6. B Q
(Inscribed angles
intercepting congruent
arcs are
congruent.)
7. RQP CBA
8. AC PR
(SAS SAS)
84 Chapter 13: Geometry of the Circle
9 a 1. BEA CED (Vertical angles are
congruent.)
2. BDC CAB (Congruent
inscribed angles)
3. BEA CED
b (i) 4 : 5 (ii)
(AA)
16 _
25
10 1. −−
BA −−−
PGD
2. DBA BDP
3. mPBD 1 _ m
2 BGD
4. mBAD 1 _ m
2 BGD
5. mPBD mDAB
6. PBD DAB
7. PBD DAB
8. PD _
BD
BD _
BA (Corresponding
sides of similar
triangles are in
11 1.
proportion.)
−−
AB is the diameter.
2. Line l is tangent to circle O.
3. ABC and AEB are right angles.
4. ABC AEB
5. CAB BAE
6. ABC AEB (AA)
7. AC _
AB
AB _
AE (Corresponding
sides of similar
triangles are in
proportion.)
12 1. −−
AC is the diameter.
2. −−
BD intersects the diameter at point E.
3. −−
AB −−
BE
4. BAE BEA
5. BEA CED
6. BAE CED
7. ABE and DCE are right angles.
8. ABE DCE
9. ABE ECD
10.
(AA)
AC _
ED _
AB
EC
11. AC EC (The product of
ED AB means equals
the product of
extremes.)
13 1. DCG CBD
2. mE 1 _ m (
2 ABC DF )
1 _ m (
2 CB )