A one is a close up door shape formed by tracing a point that move in a plane such the its street from a given allude is constant. The word circle is acquired from the Greek native kirkos, an interpretation hoop or ring. In this article, us cover the important terms related to circles, your properties, and also various circle formulas.

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In the diagram given above, O is the facility 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 the the arc

Step 3: Approach and also Working out

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

To uncover the size of the arc, we need the value of 2 variable, the center angle do by the arc and the radius.

We are currently given radius as OB = 5cmWe need to discover the ∠AOC

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

Hence, us can apply the building that the angle made at the facility by one arc is twice the inscribed angle created by the very same arc.Thus, ∠AOC = 2 × ∠ABC = 2 × 30° = 60°

Now, we recognize the main angle developed by the arc as well.

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

Thus, the exactly answer is alternative B.