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Question

A 60 angle is constructed with arc radius as 3 cm. Find the perimeter of the BOC.

A
3 cm
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B
6 cm
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C
9 cm
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D
12 cm
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Solution

The correct option is C 9 cm
Steps of construction of 60 angle:
Step 1 : Draw the given ray OA and taking O as centre and radius = 3 cm, draw an arc which intersects OA, say at a point B.
Step 2 : Taking B as centre and with the same radius, draw an arc intersecting the previously drawn arc at a point C.
Step 3 : Draw a ray OD Passing through C then BOC is the required angle of 60°.

In OBC
OB = OC [radii of same arc]
OB = BC [Arcs of equal radius]
Then OB = OC = BC = 3 cm. [Same arc with same radii]
OBC is equilateral triangle.

Perimeter of equilateral triangle
= OB + OC + BC
= 3 + 3 + 3 = 9 cm.

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