Answers

2015-10-10T19:48:15+08:00
1.)AM   ->c
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=27
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=27
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2015-10-10T20:17:35+08:00

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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.
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