To prove
Explanation of Solution
Given Information:
The Centre O lies inside the angleATP as shown below:
Formulas Used:
- Theorem(1)
The measure of an inscribed
- Theorem(2)
The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc (The Theorem is proved when the Centre Olies on the chord)
- Arc addition postulate
The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs
From the diagram given above:
Apply Theorem (2) to the chord ZT since the CentreO lies on arc ZT
.....(1)
Apply Theorem (1) to the arc AZ
Apply angle addition postulate to the angle ATP
∴
Apply arc addition postulate to the arc ANT
Substitute (1) to the Left Hand Side of (3) and (2) to Right Hand Side of (3)
Applying (4) to the (5)
Hence the theorem.
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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