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Question

Construct a ABC = 30. Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch the line AB at B and also pass through D.


A

5.5 cm

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B

2.5 cm

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C

3.464 cm

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D

6.4 cm

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Solution

The correct option is C

3.464 cm


ABC = 30 is drawn.

BE is drawn perpendicular to AB at B.

BD = 6 cm is taken from BC.

Perpendicular bisector of BD is drawn which intersects BE at O.

Taking O as centre and OB as radius a circle is drawn which pass through B and D.

In triangle BOD

OB = OD


Therefore, OBD=ODB=60

So,BOD=180OBDODB

BOD=60

All three angles of triangle BOD are equal. So it is a equilateral triangle.

Therefore, OB = OB = BD = 6cm


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