what is the relationship between the inscribed angle and its intercepted arc?
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The vertex of an inscribed angle can be anywhere on the circle as long as its sides intersect the circle to form an intercepted arc. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.
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A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at the point P enclosing an angle of 600 . The area enclosed by the tangents and the arc of the circle is, 2√3-π6 (b) √3-π3 π3-√3 (d) √3(1-π6)
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['Let the equations of the straight lines AB and CD are y = m1 x + c1 and y = m2 x + c2 respectively intersect at a point P and make angles θ1 and θ2 respectively with the positive direction of x-axis.', 'Let ∠APC = θ is angle between the given lines AB and CD.']
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Recall that a tangent to a circle is perpendicular to the diameter of the circle at the pont of tangency. Given that AC is tangent to circle O at A, this means that line AB is a diameter of the circle. Thus, angle BAC is a right angle.
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The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.
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Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure. ... Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees.
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The angle of incidence is the angle between the chord of the wing and the longitudinal axis of the airplane. ... The angle of incidence is a figure about the geometry of the plane. The angle of attack is how the wing is oriented to the wind.
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Angles in the same segment - Higher. The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.
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This will depend upon the size of the sides and the given angle. ASA i.e. when a side and any two angles are given, only one triangle can be formed. This is as if two angles are equal, third will always be equal as their sum is always 180∘ . RHS i.e. when in a right angle, hypotenuse and one side is given.
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In summary, we learned that an interior angle is an angle inside a shape, while an exterior angle is an angle made by the side of a shape and a line drawn out from an adjacent side. The sum of the interior angles of a triangle is always 180. So, if we know two angles, we can always find the third.
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Intuition states that 1/sin(x) is the same thing as sin -1 (x), just like 2 -1 is the same thing as 1/2. In case you're not familiar with arcsin, it's sort of the reverse operator of sine. You put a ratio of 2 lengths in, and you get an angle out. Same thing for arccos and arctan.
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So, the central angle is essentially the arc length multiplied by 360, the degrees of a full circle, divided by the circumference of the circle. As you can see, the arc length is simply the circumference of a circle (2πR) multiplied by the ratio of the arc angle to the full 360 angle of a circle.
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A minor arc is less than 180° and is equal to the central angle. The central angle is formed with its vertex at the center of the circle, whereas a major arc is greater than 180°. In other words, the minor arc is small while the major arc is large.
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cot(x) = 1/tan(x) , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse. arctan(x) is the angle whose tangent is x.
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1 Answer. The difference be-tween the sum of the exterior angles and the sum of the interior angles is 180∘ .
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If the lines AB and CD are parallel, then it is obvious that the co-interior angles are not equal but it turns out that they are supplementary, that is, their sum is 180° . To summarise: Co-interior angles formed from parallel lines are supplementary.
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In a plane mirror,the angle of incidence and angle of reflection are equal. The angle of incidence is the angle,created by the incident ray with the mirror surface and the angle of reflection is the angle, created by the reflected ray with the mirror surface.