Relation between Angle between "Chord and Tangent" and "Central Angle"
Question 6In ...
Question
Question 6
In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to
(A) 4 cm
(B) 2 cm
(C) 2 √3 cm
(D) 4 √3 cm
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Solution
Join OA.
We know that, the tangent at any point of a circle is perpendicular to the radius trough the point of contact. ∴∠OAT=90∘InΔOAT,Cos30∘=ATOT⇒√32=AT4⇒AT=2√3cm