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## Answers

KM ->b

AK ->a

use pythagorean theorem

c²=a²+b² or c=√a²+b²

there is already a sol'n on your pic.

2.)AM is a radius. AM is given which is 8.

all radii are congruent

given: KL=? AM=8 MK=6

sol'n:

KL=AM-MK

KL=8-6

**KL=2**

3.)AM is a radius. AM is given which is 8.

all radii are congruent

given: MD=? MB=8 BD=3

Sol'n:

MD=MB-BD

MD=8-3

**MD=5**

4.)Use Pythagorean Theorem

MD=5 ->a

MC=8 ->c

CD=? ->b

c²=a²+b²

8²=5²+b²

8²-5²=b²

64-25=b²

39=b²

√39=b

**CD=√39**

5.)Use Pythagorean Theorem

MS=8 ->c

MD=5 ->a

SD=? ->b

b²=c²-a²

b²=8²-5²

b²=64-25

b²=39

b=√39

**SD=√39**

6.)Use Pythagorean Theorem

KP=2√7 ->a

KM=6 ->b

MP=? ->c

c²=a²+b²

c²=(2√7)²+6²

c²=28+36

c²=64

c=√64

c=8

**MP=8**

7.) use Pythagorean Theorem

AM=8 ->c

KM=6 ->b

AK=? ->a

a²=c²-b²

a²=8²-6²

a²=64-36

a²=28

a=√28

a=√(4)(7)

a=2√7

**AK=2**√

**7**

8.)Use Pythagorean Theorem

AM=8 ->c

KM=6 ->b

AK=? ->a

a²=c²-b²

a²=8²-6²

a²=64-36

a²=28

a=√28

a√(4)(7)

a=2√7

**AK=2**√

**7**

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Before solving for the unknown measurements, analyze the Circle, its segments, chords, radii, and bisectors

1) Please note that AM, BM, ML, MP are radii of Circle M.

Also, if you drew a line from Center M to C, and Center M to S, MC and MS are also radii. Therefore, these segments have the same measurements.

2). When a radius bisects a chord, the radius divides the chord into two equal parts , and is perpendicular to the chord.

3) The radii/bisectors are:

MD bisects chord CS, therefore CD and DS are congruent.

MK bisects chord AP, therefore AK and KP are congruent.

Please see attached for the solution and proof/explanation.

1) Please note that AM, BM, ML, MP are radii of Circle M.

Also, if you drew a line from Center M to C, and Center M to S, MC and MS are also radii. Therefore, these segments have the same measurements.

2). When a radius bisects a chord, the radius divides the chord into two equal parts , and is perpendicular to the chord.

3) The radii/bisectors are:

MD bisects chord CS, therefore CD and DS are congruent.

MK bisects chord AP, therefore AK and KP are congruent.

Please see attached for the solution and proof/explanation.