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From Karnataka Open Educational Resources
→Problem-1
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===Interpretation of the problem===
−#O is the centre of the circle and tangents AP and AQ are drawn from an external point A.
−#OP and OQ are the radii.
−#The students have to prove thne angle PAQ=twise the angle OPQ.
−===Concepts used.===
−#The radii of a circle are equal.
−#In any circle the radius drawn at the point of contact is perpendicular to the tangent.
−#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.
−#Properties of isoscles triangle.
−#Properties of quadrillateral ( sum of all angles) is 360 degrees
−#Sum of three angles of triangle is 180 degrees.
−===Algorithm===
== 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''']]
−== Ex 4.4.2==
== Ex 4.4.2==
