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Judgement and properties of mathematical tangents
Connecting ob

∫∠ABC = 90°

∴ab is the diameter of this circle.

In △pao and △pbo.

oa=ob,po=po,pa=pb

∴△pao≌△pbo(sss)

∴∠pao=∠pbo

∫pa is the tangent of the circle.

∴∠ pao = 90 degrees (tangent property)

∴∠ PBO = 90 (equivalent substitution)

Ob is the radius of the circle.

∴pb is the tangent of the circle.

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