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have a few questions with contents of geometry book.
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1. example 17(pp97)

the solution says alternative segments are equal i.e APX = ABP, etc.
(nothing is said about AB being parallel to XY)

i dont understand this - could you point me to the relevant theory/formula, where the inscribed angle is equal to the angle formed b/w the tangent and the chord subtending this angle.

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2. same in example 19 (pp 99)
solution says MAB=BMQ
same assumption as above example 17 - where is this rule derived from - could you please point me to the theorem.

(Note this example has an error in that it is not specified that AOB is diameter and there is no basis for assuming AMB=90degrees)
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plz clarify, thanks.

O is the letter used to represent the center of a circle. So a chord AB passing through the point O has to be the diameter and hence AMB will be 90 degrees.