Preparing for the Regents Examination Geometry, AK

10. BD _
DA
11. BD _
DC
DC
_
DB
DA _
BD
( Corresponding sides of
similar triangles are in
proportion.)
12. (BD) 2 ( The product of means
DC DA equals the product of
extremes.)
13-6 Measures of Tangent
Segments, Chords and
Secant Segments
(pages 374–376)
1 (4) 20
2 (2) 46
3 (1) 17
4 (3) 24
5 (2) 10
6 (1) 3
7 (3) 25
8 (3) cz _
a
9 (3) 17
10 (3) 33
11 (1) 9
12 24
13 19
14 40
15 44
16 12
17 16
18 NQ 6, QP 16
19 x 4, GH 16
20 −−−
AOB −−−
WZ . Radius 12.5; 10 2 (7.5) 2
(12.5) 2
13-7 Circle Proofs
(pages 381–382)
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)
1 1. A is the midpoint of CD ;
−−−
AOB is a diameter.
2. CA AD
3. 1 _ m
2 CA 1 _ m
2 AD
4. mABC 1 _ m
2 AD
mABC 1 _ m
2 CA
5. mABC mABD
6. ACB and ADB are right angles.
7. mACB mADB
8. −−
AB −−
AB
9. ACB ADB (AAS AAS)
10. −−
CB −−
DB (CPCTC)
2 1. −−−
AD −−
CB
2. AD CB
3. mABD 1 _ m
2 AD
mCDB 1 _ m
2 CB
4. mABD mCDB
5. −−
DB −−
DB
6. mDAB 1 _ m
2 DB
mDCB 1 _ m
2 DB
7. mDAB mDCB
8. ADB CBD (AAS AAS)
9. −−
AB −−−
CD (CPCTC)
3 1. Circle O with diameters −−−−
MOT and −−−−
AOH
2. MAT and HTA are right angles.
3. −−−−
MOT −−−−
AOH
4. −−
AT −−
AT
5. MAT HTA (HL HL)
6. −−−
MA −−
HT
(CPCTC)
4 1. Circle O, tangents PR , PV
2. PR OR ; PV OV
3. ORP and OVP are right angles.
4. mORP mOVP
5. −−−
OR −−−
OV
6. −−
PR −−
PV
7. RPO VPO (SAS SAS)
8. RPO VPO (CPCTC)
5 1. Circle O with T as the midpoint of CH
2. m CT m TH
3. m CTH 180
4. m CT 90
5. mCOT m CT
6. COT and CTH are right angles.
7. mCOT mCTH
13-7 Circle Proofs 83