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Thepotemich [5.8K]
3 years ago
7

Given that two tangent lines are constructed from the shared point A outside a circle to the points of tangency B and C, what is

the measurement of AB if AC measures 2 cm?
A)
1
2
cm


B)
1 cm


C)
2 cm


D)
4cm
Mathematics
2 answers:
olchik [2.2K]3 years ago
6 0

Answer : 2cm

Given that two tangent lines are constructed from the shared point A outside a circle to the points of tangency B and C.

A is the external point

B and C are the point of tangency. AB and AC are the two tangent lines that meet at external point A.

The length of tangent lines from an external point is same.

So length of AB = length of AC

AC measures 2 cm so AB = 2cm



Talja [164]3 years ago
3 0
The answer would be C! Like the person stated above ''tangents to the same circle from the same point measure the same''.
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Calcula en cada caso las restantes razones trigonométricas de un angulo agudo si se conoce que:
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A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4

Explanation
The ratio for sine is opposite/hypotenuse.  This means the side opposite the angle is √3 and the hypotenuse is 5.  Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B)  The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3.  Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1.  Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D)  The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5.  Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E)  The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1.  Using the Pythagorean theorem to find the hypotenuse,
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25+1=H²
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This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse.  This means that the side adjacent the angle is 8 and the hypotenuse is 10.  Using the Pythagorean theorem to find the side opposite the angle, p:
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64+p² = 100
p² = 36
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This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.
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3 years ago
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