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# Geometry help!!

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510
3

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".

Nov 10, 2017

#1
+96106
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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

Nov 10, 2017
#2
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Wht is the answer to the other questions

Nov 12, 2017
#3
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number 1 is 5/3 because of this special formula. To find the circumradius of any triangle with sides a,b,c the formula is abc/4A where A is the area of the triangle.

Nov 13, 2017