What is the mACB if the measure of angle APB is 85 degrees?

Find the measure of APB if the measure of arc AB equals 130?

If someone is going to find the APB then they will need to know what the arch is. Because of this not being provided the answer will not be known.

Line PQ is the angle bisector of angle APB and the measurment of angle APQ equals 107?

hmm... i am not sure I understand what you are trying to ask?An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles. Therefore angle QPB is the same as APQ.

Angle subtended by an arc is double the angle subtended by it at any other point on the remaining part of the circle?

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.

What is APB in coin grading?

I don't know of any use of APB in coins or grading. ABP is occasionally used and it stands for Average Buy Price, or what a dealer would on average give for your coin.

What does locus mean in geometry?

Geometrical locus. Circle and circumferenceGeometrical locus. Mid-perpendicular. Angle bisector.Circumference. Circle. Arc. Secant. Chord. Diameter. Tangent line.Segment of a circle. Sector of a circle. Angles in a circle.Central angle. Inscribed angle. Circumscribed angle.Radian measure of angles. Round angle. Ratio ofcircumference length and diameter. Length of an arc.Huygens' formula. Relations between elements of a circle.Geometrical locus ( or simply locus) is a totality of all points, satisfying the certain given conditions.E x a m p l e 1. A midperpendicular of any segment is a locus, i.e. a totality of all points, equallyremoved from the bounds of the segment. Suppose that PO AB and AO = OB :Then, distances from any point P, lying on the midperpendicular PO, to bounds A and B of the segment AB are both equal to d . So, each point of a midperpendicular has the following property: it is removed from the bounds of the segment at equal distances.E x a m p l e 2. An angle bisector is a locus, that is a totality of all points, equally removed from the angle sides.E x a m p l e 3. A circumference is a locus, that is a totality of all points ( one of them - A ),equally removed from its center O.Circumference is a geometrical locus in a plane, that is a totality of all points, equally removed from its center. Each of the equal segments, joining the center with any point of a circumference is called a radius and signed as r or R . A part of a plane inside of a circumference, is called a circle. A part of a circumference ( for instance, AmB, Fig.39 ) is called an arc of a circle.The straight line PQ, going through two points M and N of a circumference, is called a secant ( or transversal ). Its segment MN, lying inside of the circumference, is called a chord.A chord, going through a center of a circle ( for instance, BC, Fig.39 ), is called a diameter and signed as d or D . A diameter is the greatest chord of a circle and equal to two radii ( d = 2 r ).Tangent. Assume, that the secant PQ ( Fig.40 ) is going through points K and M of a circumference. Assume also, that point M is moving along the circumference, approaching the point K. Then the secant PQ will change its position, rotating around the point K. As approaching the point M to the point K, the secant PQ tends to some limit position AB. The straight line AB is called a tangent line or simply a tangent to the circumference in the point K. The point K is called a point of tangency. A tangent line and a circumference have only one common point -- a point of tangency.Properties of tangent.1) A tangent to a circumference is perpendicular to a radius, drawing to a point oftangency ( AB OK, Fig.40 ) .2) From a point, lying outside a circle, it can be drawn two tangents to the samecircumference; their segments lengths are equal ( Fig.41 ).Segment of a circle is a part of a circle, bounded by the arc ACB and the corresponding chord AB ( Fig.42 ). A length of the perpendicular CD, drawn from a midpoint of the chord AB until intersecting with the arc ACB, is called a height of a circle segment. Sector of a circle is a part of a circle, bounded by the arc AmB and two radii OA and OB, drawn to the ends of the arc ( Fig.43 ).Angles in a circle. A central angle -- an angle, formed by two radii of the circle ( AOB, Fig.43 ). An inscribed angle -- an angle, formed by two chords AB and AC, drawn from one common point ( BAC, Fig.44 ).A circumscribed angle -- an angle, formed by two tangents AB and AC, drawn from one common point ( BAC, Fig.41 ).A length of arc of a circle is proportional to its radius r and the corresponding central angle :l = rSo, if we know an arc length l and a radius r, then the value of the corresponding central angle can be determined as their ratio:= l / r .This formula is a base for definition of a radian measureof angles. So, if l = r, then = 1, and we say, that an angle is equal to 1 radian ( it is designed as = 1 rad ). Thus, we have the following definition of a radian measure unit: A radian is a central angle ( AOB, Fig.43 ), whose arc's length is equal to its radius ( AmB = AO, Fig.43 ). So, a radian measure of any angle is a ratio of a length of an arc, drawn by an arbitrary radius and concluded between the sides of this angle, to the radius of the arc. Particularly, according to the formula for a length of an arc, a length of a circumference C can be expressed as:C = 2r,where is determined as ratio of C and a diameter of a circle 2r:= C / 2 r .is an irrational number; its approximate value is 3.1415926...On the other hand, 2 is a round angle of a circumference, which in a degree measure is equal to 360 deg. In practice it often occurs, that both radius and angle of a circle are unknown. In this case, an arc length can be calculated by the approximate Huygens' formula:p 2l + ( 2l -- L ) / 3 ,where ( according to Fig.42 ): p -- a length of the arc ACB; l -- a length of the chord AC;L -- a length of the chord AB. If an arc contains not more than 60 deg, a relative error of this formula is less than 0.5%.Relations between elements of a circle. An inscribed angle ( ABC, Fig.45 ) is equal to a half of the central angle ( AOC, Fig.45 ), based on the same arc AmC. Therefore, all inscribed angles ( Fig.45 ), based on the same arc ( AmC, Fig.45 ), are equal. As a central angle contains the same quantity of degrees, as its arc ( AmC, Fig.45 ), then any inscribed angle is measured by a half of an arc, which is based on( AmC in our case ).All inscribed angles, based on a semi-circle (APB, AQB, ..., Fig.46 ), are right angles ( Prove this, please ! ). An angle (AOD, Fig.47 ), formed by two chords ( AB and CD ), is measured by a semi-sum of arcs, concluded between its sides:( AnD + CmB ) / 2 .An angle (AOD, Fig.48 ), formed by two secants ( AO and OD ), is measured by a semi-difference of arcs, concluded between its sides: ( AnD -- BmC ) / 2 . An angle (DCB, Fig.49 ), formed by a tangent and a chord ( AB and CD ), is measured by a half of an arc, concluded inside of it: CmD / 2 .An angle (BOC, Fig.50 ), formed by a tangent and a secant ( CO and BO ), is measured by a semi-difference of arcs, concluded between its sides: ( BmC -- CnD ) / 2 .A circumscribed angle (AOC, Fig.50 ), formed by the two tangents, (CO and AO), is measured by a semi-difference of arcs, concluded between its sides: ( ABC -- CDA ) / 2 . Products of segments of chords ( AB and CD, Fig.51 or Fig.52 ), into which they are divided by an intersection point, are equal: AO · BO = CO · DO.A square of tangent line segment is equal to a product of a secant line segment by the secant line external part ( Fig.50 ): OA2 = OB · OD ( prove, please! ). This property may be considered as a particular case of Fig.52.A chord ( AB, Fig.53 ), which is perpendicular to a diameter ( CD ), is divided into two in the intersection point O :AO = OB . ( Try to prove this ! ).

What is the mACB if the measure of angle APB is 85 degrees?

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Find the measure of APB if the measure of arc AB equals 130?

Line PQ is the angle bisector of angle APB and the measurment of angle APQ equals 107?

Angle subtended by an arc is double the angle subtended by it at any other point on the remaining part of the circle?

What is APB in coin grading?

What does locus mean in geometry?

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Find the measure of APB if the measure of arc AB equals 130?

Line PQ is the angle bisector of angle APB and the measurment of angle APQ equals 107?

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