Changes
From Karnataka Open Educational Resources
624 bytes removed
, 09:34, 12 August 2014
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| == Problem-1== | | == Problem-1== |
| #Tanjents AP and AQ are drawn to circle with centre O, from an external point A. Prove that ∠PAQ=2.∠OPQ <br> | | #Tanjents AP and AQ are drawn to circle with centre O, from an external point A. Prove that ∠PAQ=2.∠OPQ <br> |
− | [[File:fig1.png|200px]] | + | [[http://karnatakaeducation.org.in/KOER/en/index.php/Class10_circles_tangents_problems '''Solution''']] |
− | ===Interpretation of the problem===
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− | #O is the centre of the circle and tangents AP and AQ are drawn from an external point A.
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− | #OP and OQ are the radii.
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− | #The students have to prove thne angle PAQ=twise the angle OPQ.
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− | ===Concepts used.===
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− | #The radii of a circle are equal.
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− | #In any circle the radius drawn at the point of contact is perpendicular to the tangent.
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− | #The tangent drawn from an external point to a circle a] are equal b] subtend equal angle at the centre c] are equally inclined to the line joining the centre and extrnal point.
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− | #Properties of isoscles triangle.
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− | #Properties of quadrillateral ( sum of all angles) is 360 degrees
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− | #Sum of three angles of triangle is 180 degrees.
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− | ===Algorithm===
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| == Ex 4.4.2== | | == Ex 4.4.2== |