SOLUTION: Drawn in a circle whose radius is 12 cm, chord AB is 16 cm long. Calculate the angular size of minor arc AB.

Question 1157991: Drawn in a circle whose radius is 12 cm, chord AB is 16 cm long. Calculate the angular
size of minor arc AB.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

Perpendicular to chord from centre bisects chord
AD=BD=8
Triangle AOD right triangle
By Pythagoras theorem
12^2= 8^2+OD^2
OD = 4sqrt(5)
tan B = 4sqrt(5)/8 = 1.12
Angle B = 48.2 ~48 deg
In triangle AOD
angle A +angle AOD +angle ODA =180 deg
48+90+AOD =180
Angle AOD =42 deg
Angle AOC = 2* 42 =84
84 is central angle
Measure of arc AC =84 degrees

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Drawn in a circle whose radius is 12 cm, chord AB is 16 cm long. Calculate the angular
size of minor arc AB.

With center O, and altitude OD drawn from center to chord, we get cos ∡OAD =
∡OBD also = 48.19^o
Therefore, central ∡AOB = 180 - 2(48.19^o) = 180 - 96.38^o = 83.62^o
From this, we can see that
That's ALL!!
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