In the given figure, the side BC of a ? ABC is produced on both sides. Then ? 1 + ? 2 is equal to :

From above figure , we can see that
Join B and D and produce BD to E
Then, p + q = ? and s + t = x
We know that , Exterior angle = Sum of two interior angle
Now, s = p + ? (Exterior angle of a ? prop.)
Similarly, t = q + ? (Exterior angle of a ? prop.)
Adding, s + t = p + q + ? + ?
Putting s + t = x and p + q = ? ,
Hence x = ? + ? + ?

We know that In center of every triangle ( acute , obtuse and right angle ) lies in its interior.
Hence required answer will be any triangle .

From given figure , we have
In quadrilateral ABCD , we can see that
Diagonal AB = Diagonal CD ......... ( ? )
AO = OB ......... ( ? )
DO = CO ......... ( ? )
?DOB = 90° ......... ( ? )
From ( ? ) , ( ? ) , ( ? ) and ( ? ) , we get
From above , it is clear that In quadrilateral ABCD , diagonals are equal and they bisect each other at 90° .
? Quadrilateral ABCD is square.

From given figure , we have
Let, (x + 1) be the hypotenuse and perpendicular = x - 1 , base = x.
By pythagoras theorem ,
? (x + 1)² = x² + (x + 1)² ? x = 4
? Hypotenuse = 4 + 1 = 5

The circumcentre of a triangle is always the point of intersection of the Bisectors .Hence required answer will be bisectors .