A one is a closed shape developed by tracing a suggest that moves in a airplane such the its street from a given suggest is constant. Words circle is derived from the Greek word kirkos, an interpretation hoop or ring. In this article, us cover the essential terms related to circles, your properties, and various circle formulas.

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In the diagram provided above, O is the center of the circle. If OB = 5 cm and ∠ABC = 300 climate what the length of the arc AC?

5π/65π/35π/25π10πSolution

Step 1: Given

OB = 5 cm∠ABC = 30°

Step 2: to find

Length that the arc

Step 3: Approach and Working out

Length that the arc = (Central angle made by the arc/360°) × 2 × π × R.

To find the length of the arc, we require the worth of 2 variable, the facility angle made by the arc and also the radius.

We are already given radius together OB = 5cmWe need to discover the ∠AOC

On visualizing the diagram, the inscribed angle by the arc AC is ∠ABC, and also the facility angle by arc AC is ∠AOC.

Hence, we can use the home that the angle made at the center by one arc is double the inscribed angle created by the exact same arc.Thus, ∠AOC = 2 × ∠ABC = 2 × 30° = 60°

Now, we know the central angle formed by the arc together well.

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Hence, size of the arc AC =(Central edge made by the arc/360°) × 2 × π × R.=(60°/360°) × 2 × π × 5.=(1/6) × 2 × π × 5.=(5π/3) cm

Thus, the correct answer is choice B.