1)
The sides of 
have lengths 
, , and 
. What is the circumradius of ?
2)
Let 
and 
be the circumcenter and orthocenter of acute triangle , respectively. If 
, what is 
in degrees?
3)
In , the circumcenter and orthocenter are collinear with vertex 
. Which of the following statements must be true?
(a) must be an isosceles triangle.
(b) must be an equilateral triangle.
(c) must be a right triangle.
(d) must be an isosceles right triangle.
Enter your answer as a comma-separated list. If there is no correct option, write "none".
+128408 1) The circumradius is given by
[ Product of the sides ] / [ 4 * Area ]
The area is given by (1/2) Base * Height
This ttriangle is isosceles....let the base = 2 units
The height [altitude ] is given by √ [ (√ 10)^2 - 1^2 ] = √ [ 10 - 1 ] = √ [9] = 3 units
So...the area is (1/2) 2 (3) = 3 units^2
So....the circumradius is [ √10 * √10 * 2 ] [ 4 * 3] = [ 20/12] = 5/3 units ≈ 1.67 units
