Question

in the following figure BC= radius OB find the value of angle OCB

Answer 1

23 is correct answer

Answer 2

The value of the same OCB according to the given diagram is 23 degrees.

Given :

BC = Radius of the circle i.e. OB

Angle AOD = 69 degree

To Find :

The value of the angle OCB

Solution :

Calculations for the triangle AOB :

The sides OA and OB are the radius of the circle and thus the same.

Let the angle OAB be "y".

As OA = OB,  $OAB = OBA = y$

Equation 1 :         $OAB + OBA + AOB = 180$

                           $AOB = 180 - OAB - OBA$

                           $AOB = 180 - y - y$

                           $AOB = 180 - 2y$

Calculations for the triangle BOC :

The sides BC and OB are the same as the radius of the circle.

Let the angle BOC be "x".

As BC = OB,  $BOC = BCO = x$

Equation 2 :        $BOC + OCB + OBC = 180$

                           $OBC = 180 - BOC - BCO$

                           $OBC = 180 - x-x$

                           $OBC = 180 - 2x$

Angles ABO and OBC are complementary angles, thus

Equation 3 :         $180 - 2x + y = 180$

                             $y = 2x$

Angles AOD, AOB, and BOC are complementary angles, thus

Equation 4 :         $69 + (180 - 2y) + x = 180$

                            $69 - 2y + x = 0$

                            $2y - x = 69$

Combining Equations 3 and 4 from above, we get :

                            $2(2x) - x = 69$

                            $3x = 69$

                            $x = 23$

Hence, the value of the angle OCB i.e. x is 23 degrees.

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