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# Arc

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6   I could not figure this out if my life depended on it. I have over 40 of these questions and I'm so confused. Please help and show work because I really need to understand this.

Sep 16, 2019

#1
+2

I'll try a few

In the first one.....these chords have the same length....so....this implies that

(7x - 39)°  = 87°

7x - 39   = 87      add 39 to both sides

7x  =  126        divide both sides by 7

x  = 18   Sep 16, 2019
#5
0

I thought I was supposed to some special way to solve the arc ones. So I just solve the arc and line questions the same way?

Guest Sep 16, 2019
#2
+2

Second one.....same thing.....the chords LM and NP have the same length

So

41 - 2x  = 7x  +  5         add  2x to both sides.....subtract 5 from both sides

36  = 9x      divide both sides by  9

4   = x

So

LM  = 41 - 2x   =   41 - 2(4)   =  41  - 8   =   33   Sep 16, 2019
#3
+2

Third one

Since chords  DE  = GF....equal chords are the came distance from the center of the circle

This implies that  HJ  = JI   ....so....

3x + 20  =  15x  - 64         add 64 to both sides, subtract 3x from both sides

12x  = 84    divide both sides by 12

x  = 7

So JI   = 15x - 64  =  15(7) - 64  =  105 - 64  = 41   Sep 16, 2019
#4
+2

Fourth one

LM and NP  are equal distances from the center of the circle....so....they have equal length

Then.....they also span the same arcs

This implies that

(8x - 56)°  = (5x + 22)°

8x - 56  =  5x + 22          add 56  to both sides, subtract 5x from both sides

3x =  78      divide both sides by 3

x  =  26

So  LM spans an arc of   8(26) - 56  = 208 - 56  = 152°

And NP spans the same arc

So  LP  spans an arc  = 360 - LM - NP - MN =

(360 - 152  -152  - 39)°   =    17°   Sep 16, 2019
#6
+2

Last one

Equal segments drawn from the center of the circle meet chords BC and CD at right angles

This means that the two chords are equal and thus, they span the same arcs....so....like before...

9x - 53  = 2x + 45     add 53 to both sides  and subtract 2x form both sides

7x = 98     divide both sides by 7

x  = 14

So  each chord spans an arc of  9(14)  - 53  = 73°

Then BAD  will span  an arc  =  360 - 73 - 73   = 214°   Sep 16, 2019