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Arisa [49]
3 years ago
9

PLEASE HELP DETAILS ARE BELOW I WILL RATE BRAINIEST CHORD AND ARCS FIND THE MEASURE OF ARC CD DETAILS BELOW

Mathematics
2 answers:
Ira Lisetskai [31]3 years ago
8 0

Wouldn’t it be 36.7 because that’s the arch am I right?

kaheart [24]3 years ago
6 0

Answer:

The measure of arc CD is 114.6°.

Step-by-step explanation:

Let the center of the circle be O and OP is perpendicular to CD at point point P.

The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.

CP=\frac{CD}{2}=\frac{36.7}{2}=18.35

In a right angles triangle,

\sin\theta =\frac{opposite}{hypotenuse}

In a right angles triangle OPC,

\sin\angle POC =\frac{18.35}{21.8}

\angle POC =\sin^{-1} (\frac{18.35}{21.8})

\angle POC \approx 57.3

In triangle OPC and OPD,

OC=OD                  (Radius)

OP=OP                  (Reflexive property)

CP=DP                   (Altitude on chord from center)

By SSS postulate

\triangle OPC\cong \triangle OPD

\angle POC\cong \angle POD                      (CPCTC)

\angle POC=\angle POD

The measure of angle COD is

\angle COD=\angle POC+\angle POD

\angle COD=2\angle POC

\angle COD=2(57.3)

\angle COD=114.6

Therefore the measure of arc CD is 114.6°.

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