Question

answer the following

1. How to find rational number between two irrational number

2. refer to pic both the question one is in paper and another one is on my rough notebook please show methods also


answer this questions

Answer 1

For the angle question:
Since BO and CO are bisectors,<EBO=<OBC=a(assumption)
Similarly <DCO=<OCB=b(assumption)
Now,y+2a=180...a=90-y/2
Similarly, b=90-z/2... where z is the angle ACB
Now,a+b+<BOC=180
90-y/2+90-z/2+<BOC=180
<BOC=(y+z)/2
x+y+z=180...y+z=180-X substitute this value in above
<BOC=(180-x)/2 = 90 -1/2<BAC...hence proved