TAR is a tangent to the circle at A. If angle BTA=20 and angle BAT=28 then find angle DAR. (Here, TBD is a secant)
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We know, that radius is perpendicular to a tangent .
∴ ∠OPR=90
o
⇒ ∠OPQ+∠QPR=90
o
⇒ ∠OPQ+50
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=90
o
⇒ ∠OPQ=90
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−50
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⇒ ∠OPQ=40
o
⇒ OP=OQ [ Radii of a circle ]
⇒ ∠OPQ=∠OQP=40
o
[ Base angles of equal sides are also equal ]
In △POQ,
⇒ ∠OQP+∠POQ+∠OPQ=180
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[ Sum of angles of a triangle is 180
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]
⇒ 40
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+∠POQ+40
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=180
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⇒ ∠POQ+80=180
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⇒ ∠POQ=100
o
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