Question

In a circle with centre o. Ad is a diameter and ac is achord b is point on ac, such that ob=5cm and angle oba=60 degree in angle doc =60 degree, then what is the length of bc

Answer 1

Answer:

Given, OB = 5cm, angle OBA = 60°

angle OBA is subtended by minor arc CD and the same arc subtends angle CAD on the remaining part of the circle. So, angle CAD = 30°.

By angle sum property of triangle AOB, angle BOA = 90°

By linear pair, angle OBC = 120°

By linear pair axiom, angle COB = 30°

By angle sum property of triangle BOC, angle BCO = 30°

NOW, BOC IS AN ISOSCELES TRIANGLE

SO BC = 5cm