and are chords perpendicular to each other. The radius of the circle is 7 cm. Find the sum of the length of the arcs and .
Use = .
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S o l u t i o n :
Let's say, E is the intersection of A B and C D . We know that ∠ C E B = 2 1 ∗ ( A r c C B + A r c A D )
--> A r c C B + A r c A D = 1 8 0 d e g r e e s .
This means, the length of A r c C B + A r c A D is simply h a l f of the circumference. C = ( 7 ) ( 2 ) ( π ) = 1 4 π .
Therefore, A r c C B + A r c A D = C / 2 = 7 π u n i t s − > 7 ∗ 7 2 2 − > 2 2 u n i t s
− − − − − − − − − − − − − − − − −
N o t e :
A whole c i r c u m f e r e n c e varies directly as the w h o l e sum of the angles in the circle or in short,
C = 3 6 0 k
In our situation, C = 1 4 π − − > 1 4 π = 3 6 0 k
In the other hand, C = 1 8 0 k
by using ratio and proportion, we obtain C = 7 π or in conclusion, 7 π − > 7 ∗ 7 2 2 − > 2 2 u n i t s is the s u m of the lengths of Arc CB & Arc AY.