m BED m BD and m ABE m AE. Apply the Ext. Thm. to BCE to prove that m C Answers for Lesson 12-4, pp Exercises Geometry Chapter

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1 Answers for Lesson -4, pp Exercises x 6; y x 5; y x 8; y x 5.8; y.4 4. x 5.3; y.9 5. about 7.8 ft 6. It could range from 56.9 ft to 85. ft x 8. 8 x 9. 8 y x.7; y 4. x 8.9; y 5. x.9; y.3 6. ou must use (7.5 6)6 or the entire segment length , 4, 86, a. 3; 3 m 8; mz 3 b. If the measure is 3, the ship is safe. 9. Answers may vary. Sample: Since they are inscribed ': mbed m BD and mabe m AE. Apply the Ext. Thm. to BCE to prove that mc (mae m BD ). Geometry Chapter 73

2 Answers for Lesson -4, pp Exercises (cont.) 3. Given: AB tangent to (O at A, BC tangent to (O at C; Prove: mb (36 m AC ).. Construct AC.. ma m AC (The measure of an formed by a 3. mc m AC (The measure of an formed by a 4. mb 8 ma mc ( Sum Thm.) 5. mb 8 mac m AC (Subst.) 6. mb 8 mac 7. mb (36 m AC ) (Distr. Prop.) Given: BC secant and AB tangent to (O. AB, BC intersect at B and AB tangent to (Oat A. BC intersects (O at D; Prove: mb (mac m DA ).. Construct AD.. ma m AD (The measure of an formed by a 3. madc m AC (The measure of an inscribed is half the measure of its 4. mb madc mbad (Subtr. and Ext. Thm.) 5. mb mac m AD (Subst.) 6. mb (mac m AD ) (Distr. Prop.) Geometry Chapter 74

3 Answers for Lesson -4, pp Exercises (cont.) 3. Given: A circle with secant segments V and ZV; Prove: V? WV ZV? V.. Construct and ZW.. V ZVW (Reflexive Prop. of ) 3. V WZV ( inscribed ' that intercept the same arc are.) 4. V ZVW (AA) V ZV 5 WV V 5. (In similar figures, corr. sides are proport.) 6. V?WV V?ZV (Mult. Prop.) 3. Given: A circle with tangent TV and secant V; Prove: V?V (TV).. Construct T and T.. mtv m T (The measure of an inscribed is half the measure of the 3. mvt m T (The measure of an formed by a chord and a tangent is half the measure of the 4. mtv mvt (Trans. Prop. of ) 5. TV TV (Reflexive Prop. of ) 6. TV VT (AA) V TV 5 V TV 7. (In similar figures, corr. sides are proport.) 8. V?V TV (Mult. Prop.) Z W T V V Geometry Chapter 75

4 Answers for Lesson -4, pp Exercises (cont.) 33. Answers may vary. Sample: If the given pt. is on the circle, then a line through the given pt. can only intersect the circle tangentially or one other place. It follows that one segment has length zero, so the product of the segments is always zero m mqrp m PQ ( diff. of intercepted arcs). m mpq mqrp m PQ (Add. Prop. of and Distr. Prop.) 3. m mpq (mqrp m PQ ) (Distr. Prop.) 4. m mpq (36) (circle has 36 ) 5. m mpq 8 (Subst.) 35.. m mqrp mpq Q diff. of intercepted arcsr. m mrqp m RP Q diff. of intercepted arcsr 3. m m mqrp mrqp mpq m RP (Subst.) 4. m m mqr m RP mqr mpq mpq m RP (Arc. Add. Post. and Distr. Prop.) 5. m m m QR (Distr. Prop.) 36.. (PQ) (QS)(QR) (Prod. of segments is const.). b (c a)(c a) (Subst.) 3. b c a (Distr. Prop.) 4. b a c (Add. Prop. of ) Geometry Chapter 76

5 Answers for Lesson -4, pp Exercises (cont.) 37. A O B mab mbc mac, since chords AB, BC, and CA are all. So the measures of,, and Z are (4 ) 6, and Z is equilateral. C Z Geometry Chapter 77

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