A circle is shown. 2 tangents intersect at a point outside of the circle to form an angle with a measure of 70 degrees. The tang
2 answers:
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Answer:
The only equation which is incorrect is in option B.
Step-by-step explanation:
Eva used the following equation in order to solving integers, which is
⇒ ......... (1)
Now, if the equation Ava used is correct, then we have to find which of the given equations is not correct.
Now, in option A) it is given that
⇒ which is same as equation (1).
In option B) it is given that
⇒ which is not same as equation (1).
In option C) it is given that
⇒ which is same as equation (1).
Again, in option D) it is given that
⇒ which is same as equation (1).
Therefore, the only equation which is incorrect is in option B. (Answer)
Answer:
- The three heights are 4.8, 6, 8
- The three medians are 5, 2√13, √73
- The three angle bisectors are (24/7)√2, 3√5, (8/3)√10
- The radii of the incircle and circumcircle are 2 and 5, respectively
Step-by-step explanation:
a) The other leg of the right triangle is ...
b = √(10² -6²) = √64 = 8
The area of the triangle is ...
A = 1/2bh = 1/2(6)(8) = 24
Then the height to the long side is ...
h = 2A/c = 48/10 = 4.8
The three heights are 4.8, 6, 8.
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b) The medians to the hypotenuse is half its length, because that is also the radius of the circumcircle: 10/2 = 5.
The medians to the legs are computed from the Pythagorean theorem:
median to "b" = √(4² +6²) = √52 = 2√13
median to "a" = √(3² +8²) = √73
The three medians are 5, 2√13, √73.
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c) The angle bisectors to the legs can be found in a fashion similar to the medians, using the angle bisector theorem to locate the point of intersection on the leg.
The angle bisector to "b" divides it into segments in the ratio 6:10, so the point of intersection is 6/(6+10)×8 = 3 units from the right angle. Then its length is ...
bisector to "b" = √(6² +3²) = √45 = 3√5
The angle bisector to "a" divides it into segments in the ratio 8:10, so the point of intersection is 8/(8+10)×6 = 8/3 units from the right angle. Then its length is ...
bisector to "a" = √(8² +(8/3)²) = (8/3)√10
I find it easier to compute the bisector to the hypotenuse by considering the hypotenuse to be a line with x- and y-intercepts at 8 and 6. Then its equation can be 3x+4y=24, and its intersection with the line y=x will be x = y = 24/7. The length of the segment to that point is ...
bisector to "c" = (24/7)√2
The three angle bisectors are (24/7)√2, 3√5, (8/3)√10.
__
d) The radius of the inscribed circle can be found from the formula ...
r = √((s-a)(s-b)(s-c)/s) . . . . where s is the semiperimeter = 24/2 = 12
r = √(2×4×6/12) = 2
The hypotenuse is the diameter of the circumscribed circle, so the radius of that circle is c/2 = 5.
The radii of the incircle and circumcircle are 2 and 5, respectively.
