Question

prove that angle BAC -angle obc =90 degree

Answer 1

Please refer the above photograph for the used process.

KEY POINTS TO REMEMBER :-

☸️ Angle subtended by a chord at the centre is double the angle subtended by it at any other part of the circle.   ...... (i)

For Example -  If a chord subtends x° at Centre and y° at any other part of the circle.

Then,  x = 2y

☸️ Angle sum property of a triangle is 180°

...... (ii)

☸️ COMPLETE ANGLE :-

     The angle around any point which forms a complete circle and whose sum is 360 degrees is known as a complete angle. ..... (iii)

☸️ SUBSTITUTION :-

    It is a process of substitution of value of any one variable from first equation into the second equation.

☸️ SOLUTION :-

 z = 2x    ( Reason = (i))

Now,

  z + t = 360 °

Or,   t = 360 -  z

Also,

  t = 360 - 2x

Now,

In triangle OBC :-

y + y + t = 180

2y + 360 -  2x = 180

2y -  2x = 180 -  360 = (-180)

Or,

2x -  2y = 180

2(x-y) = 180

  x -  y = 180 /2 = 90

So,

 Angle BAC -  Angle OBC = 90 degrees.

Hence, Proved!

Thanks!