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From Karnataka Open Educational Resources
→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]]
[[File:fig1.png|200px]]
===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.
== Ex 4.4.2==
== Ex 4.4.2==
