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$1 to $3 depending upon the condition of the token.

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Q: What is the value of a misprint opa red coin point?
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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?

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 o-phthaldehyde?

O-phthaldehyde (OPA) is a small fluorscent molecule that reacts with primary amines, predominantly lysines and N-termins amines, in aqueas solutions at room temperature. It is used to determine the total concentration of protein in a sample. OPA can be used within a concentration of 1µg/ml - 1 mg/ml. Because it will react with N-terminus amines, it is a good choice for assays of small peptides that may not have enough amino acids to be detected by Bradford, BCA or Lowry protein assays.