Math Teaching on Properties of Circles

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Properties of Circles

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Tuesday, July 21, 2009

Teaching Concept Eleven

Let us look at the last Property of the Circle:
- The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

- How to proof if the angle between a tangent and a chord through the point of contact is always equal to the angle in the alternate segment.
Proof:
- angle SPT= 90° (right angle in a semicircle)
- angle x+ angle y = 90° (angle sum of triangle)
- angle y+ angle z= 90° (tangent perpendicular to radius)
- angle x= angle z
- angle PTB= angle PST
- angle PST= angle PQT ( angles in same segment)
- angle PTB= angle PQT

- Let us try some simple questions:

- In the figure shown, line PA and line PB are tangents to the circle. angle ABP= 60° and BAC= 40°. Find the value of angle x and angle y.

- Calculate the value of angle x and angle y.

# posted by Properties of Circles at 6:32:00 AM