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Angle subtended by an arc is double the angle subtended by it at any other point on the remaining part of the circle?
Wiki User
∙ 14y ago
You can prove this just from knowing that the three angles of a triangle add to 180 degrees.
Label the ends of the arc A and B, the circle's centre O and the "any other point" P.
We want to show that angle APB is half of angle AOB.
(This uses the notation where you write three letters XYZ to mean the angle formed between straight lines XY and YZ).
Consider the triangle formed by O, B and P. The lengths OB and OP are the same (the radius of the circle). This means that the triangle is isosceles and angles OPB and OBP are the same.
Since POB + OPB + OBP = 180 degrees
and OPB = OBP
we have POB + 2 * OPB = 180
With the same working, the triangle formed by O, A and P gives us
POA + 2 * OPA = 180
Subtract these two equations:
(POB - POA) + 2 * (OPB - OPA) = 180 - 180 = 0
Rearrange:
2 * (OPB - OPA) = POA - POB
If you draw a diagram you will see that OPB - OPA = APB
and POA - POB = AOB
so we have 2 * APB = AOB as required.
Wiki User
∙ 14y ago
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If an arc subtend angle of 75 what is angle subtended by it on remaining part of circle?
360 - 75 = 285
An angle subtended by an arc is double at the center?
an angle subtended by an arc is double at the center
What do you call the angle whose vertex is at the center of the circle and whose sides are the radii of the circle?
It is the subtended angle of the arc
What is the value of the degree of an angle in a semi-circle?
An angle subtended at the semicircular arc is 90 degrees.
What is an angle whose vertex whose vetex is the center of a circle?
It will be the same angle subtended by its circumference.
If an arc subtend angle of 75 what is angle subtended by it on remaining part of circle?
360 - 75 = 285
An angle subtended by an arc is double at the center?
an angle subtended by an arc is double at the center
What do you call the angle whose vertex is at the center of the circle and whose sides are the radii of the circle?
It is the subtended angle of the arc
What is an arc central angle and radius of the circle?
Radius: A line from the center of a circle to a point on the circle. Central Angle: The angle subtended at the center of a circle by two given points on the circle.
What is the value of the degree of an angle in a semi-circle?
An angle subtended at the semicircular arc is 90 degrees.
What is an angle whose vertex whose vetex is the center of a circle?
It will be the same angle subtended by its circumference.
Why is an inscribed angle that intercepts a semi-circle a right angle?
It is the consequence of one of the circle theorems and in some books, it is considered a theorem itself. The underlying proposition is that the angle subtended at the circumference of the circle by any arc of a circle is half the angle subtended at the centre. In the case of a semicircle, the arc is the half circle and the angle at the centre is the one that the diameter makes at the centre of the circle ie 180 degrees. So the angle at the circumference is half that ie 90 degrees.
What is a 90 degree angle subtended by?
May things, but the probable answer sought here is a diameter of a circle, at the circumference of the circle.
When a triangle with one side length the diameter of a circle is inscribed in that circle does it have to be a right triangle?
Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.
Explain the difference between a central angle and an inscribed angle?
A central angle has its vertex at the center of a circle, and two radii form the Arms. Central angle AOC is described as subtended by the chords AC and by the arc AC. An inscribed angle has its vertex on the circle, and two chords form the arms. Inscribed angle ABC is also described as subtended by the chord AC and by the arc AC.
How do you find radius when arc length is given?
Let us recall the formula for the circumference of a circle. That one is 2pi r. r is the radius of the circle and 2pi is the angle in radian measure subtended by the entire circle at the centre. If this is so, then any arc length 'l' will be equal to the product of the angle in radian measure subtended by the arc at the centre and the radius.So l = theta r. Say theta is the angle subtended by the arc at the centre.Therefrom, r = l / Theta.
Find the length of arc subtended by a central angle of 30 degrees in a circle of radius of 10 cm?
5.23
