SOLUTION: Hello I want to prove this T.T but i dont know how I need to draw this diagram and prove it!
Two circles intersect at points A and B. From any point P on the line AB, tangents P
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-> SOLUTION: Hello I want to prove this T.T but i dont know how I need to draw this diagram and prove it!
Two circles intersect at points A and B. From any point P on the line AB, tangents P
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Question 1031420: Hello I want to prove this T.T but i dont know how I need to draw this diagram and prove it!
Two circles intersect at points A and B. From any point P on the line AB, tangents PQ and PR are drawn to the circles. Prove that PQ=PR.
Thank you! Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
Hello I want to prove this T.T but i dont know how I need to draw this diagram and prove it!
Two circles intersect at points A and B. From any point P on the line AB, tangents PQ and PR
are drawn to the circles. Prove that PQ=PR.
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We are given two circles with the centers O1 and O2 intersec-
ting in the common points A and B (see the Figure on the right).
The straight line AB is drawn through the points A and B.
The point P is an arbitrary point in this straight line.
The tangent lines PQ and PR are drawn from P to the circles O1
and O2 respectively. Q and P are the tangent points.
We need to prove that the tangent segments PQ and PR are
congruent: |PQ| = |PR|.
The key for the proof is this Theorem of the school Geometry:
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If a tangent and a secant lines are released from a point
outside a circle, then the product of the measures
of the secant and its external part is equal to the square
of the tangent segment.
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