Congruent Circles If the diameter or radius of one circle is the same as another circle, they are congruent. Likewise, if the circumference for two circles is the same, the circles are congruent.

The symbol ≡ means “is congruent to”. Two triangles are similar if they have the same shape. Two similar triangles are equiangular, i.e., angles which correspond are equal.

Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference.

In a circle or congruent circles, congruent arcs are arcs with equal measures.

• Circle Theorem 1 – Angle at the Centre.
• Circle Theorem 2 – Angles in a Semicircle.
• Circle Theorem 3 – Angles in the Same Segment.
• Circle Theorem 4 – Cyclic Quadrilateral.
• Circle Theorem 5 – Radius to a Tangent.
• Circle Theorem 6 – Tangents from a Point to a Circle.
• Circle Theorem 7 – Tangents from a Point to a Circle II.

How do you calculate arc length without the angle?

1. Divide the chord length by double the radius.
2. Find the inverse sine of the result.
3. Double the result of the inverse sine to get the central angle in radians.
4. Once you have the central angle in radians, multiply it by the radius to get the arc length.

A major arc is an arc larger than a semicircle. A central angle which is subtended by a major arc has a measure greater than 180°. A semi-circle is associated with half of a rotation which is 180°. Minor arcs are associated with less than half of a rotation, so minor arcs are associated with angles less than 180°.

If you want to indicate the major arc, add an extra point and use three letters in the name. For example in the diagram above, the major arc is indicated by which is the long arc from A to B going around the bottom via K.

An arc of a circle is any portion of the circumference of a circle. To recall, the circumference of a circle is the perimeter or distance around a circle. Therefore, we can say that the circumference of a circle is the full arc of the circle itself.

diameter

In order to prevent confusion, major arcs are always named with three letters; the letters that denote the endpoints of the arc and any other point on the major arc. When referring to the measure of an arc, always place an “@$/begin{align*}m/end{align*}@$” in from of the label.

Answer Expert Verified Name an angle with three letters, where the middle letter is the vertex of the angle, and the other two letter as the non-collinear points in the angle. The angle is also named with a letter representing the vertex. In example above, ∠ABC can also be written as ∠B.

The parts of the arch are:

• The absolute top of the arch is the apex.
• The curve at the top of the arch is known as the crown.
• The point at which the curve begins is the springing or spring-line.
• The curve between the springing and the crown is known as the haunch.
• The inner curve of the arch is the intrados.

Arc and arc functions. An arc function undoes a trig or hyperbolic trig function. This function returns only one answer for each input and it corresponds to the blue arcsine graph at the left. Arcsine may be thought of as “the angle whose sine is” making arcsine(1/2) mean “the angle whose sine is 1/2” or /6.

denotes an inverse function, not the multiplicative inverse. The principal value of the inverse cotangent is implemented in the Wolfram Language as ArcCot[z]. This definition is also consistent, as it must be, with the Wolfram Language’s definition of ArcTan, so ArcCot[z] is equal to ArcTan[1/z].

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Terms in this set (6)

• sin. 1/csc.
• cos. 1/sec.
• tan. 1/cot.
• cot. 1/tan.
• sec. 1/cos.
• csc. 1/sin.