The measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Option C is correct.
What is the measure of arc made by parallel chord?
The measure of arc made by parallel chord in a circle are equal in measure.
The arc made by chord BC is,
arc BC=8x-46° .....1
The arc made by chord AD is,
arc AD=5x+26° .......2
The chord AD and BC are equal. Thus, the arc made by them should be equal. Thus,
arc BC=arc AD
8x-46°=5x+26°
Simplify it further,
8x-46°=5x+26°
8x-5x=26+46
3x=72
x=(72/3)
x=24°
Put the value of x in equation 1,
arc BC=8x-46°
arc BC=8(24°)-46°
arc BC=192°-46°
arc BC=146°
Thus, the measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Option C is correct.
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