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How do you calculate the arc length of a circle?

Arc length = 2πr (θ/360) θ = the angle (in degrees) subtended by an arc at the center of the circle. 360 = the angle of one complete rotation. From the above illustration, the length of the arc (drawn in red) is the distance from point A to point B.

How do you find the angle of an arc?

An arc measure is an angle the arc makes at the center of a circle, whereas the arc length is the span along the arc. This angle measure can be in radians or degrees, and we can easily convert between each with the formula π radians = 180° π r a d i a n s = 180 ° .

What is the degree measure of an arc?

Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. For example, an arc measure of 60º is one-sixth of the circle (360º), so the length of that arc will be one-sixth of the circumference of the circle.

Why are inscribed angles half the arc?

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. Therefore the measure of the angle must be half of 180, or 90 degrees.

How do you find the radius of an inscribed triangle?

For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=Ks=√s(s−a)(s−b)(s−c)s.

What is the radius of the incircle of a triangle?

Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides).

How do you find the radius of an Incircle of a right angled triangle?

Approach: Formula for calculating the inradius of a right angled triangle can be given as r = ( P + B – H ) / 2. And we know that the area of a circle is PI * r2 where PI = 22 / 7 and r is the radius of the circle.

What is the radius of Incircle of equilateral triangle?

, where r is the radius of given circle. Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3.

What is Circumradius and Inradius of a triangle?

Inradius The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. Circumradius: The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.

What is Circumcircle of Triangle?

The circumcircle is a triangle’s circumscribed circle, i.e., the unique circle that passes through each of the triangle’s three vertices. The center of the circumcircle is called the circumcenter, and the circle’s radius is called the circumradius.

What is the ratio of radius of Incircle to Circumcircle?

Answer. What is ratio of radius of circumcircle to the radius of in circle of an equilateral triangle? Both circles have the same center. = (2/1).

What is Circumradius of a right triangle?

Right triangles The hypotenuse of the triangle is the diameter of its circumcircle, and the circumcenter is its midpoint, so the circumradius is equal to half of the hypotenuse of the right triangle.

What is the measure of the Circum radius of a triangle whose sides are 9 40 and 41?

9-40-41 is a Pythagorean triplet. In a right angled triangle, the circum radius is half the hypotenuse. In the given triangle, the hypotenuse = 41. Therefore, the circum radius = 412 = 20.5 units.

What is Orthocentre of a triangle?

The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle.

Is Orthocenter and Circumcenter same?

The centroid is always between the orthocenter and the circumcenter. The distance between the centroid and the orthocenter is always twice the distance between the centroid and the circumcenter. The orthocenter is always outside the triangle opposite the longest leg, on the same side as the largest angle.

How do you find the Orthocenter given vertices?


  1. Find the equations of two line segments forming sides of the triangle.
  2. Find the slopes of the altitudes for those two sides.
  3. Use the slopes and the opposite vertices to find the equations of the two altitudes.
  4. Solve the corresponding x and y values, giving you the coordinates of the orthocenter.

How do you find the Incenter?

Simply construct the angle bisectors of the three angles of the triangle. The point where the angle bisectors intersect is the incenter. Actually, finding the intersection of only 2 angle bisectors will find the incenter. Finding the third angle bisector, however, will ensure more accuracy of the find.