Question

In figure AB is a chord of a circle and At is a tangent at A such that angle BAT = 60° find
measure of angle acb
​

Answer 1

Answer:

120°

Step-by-step explanation:

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Given: AB is chord of circle, AT is tangent to circle at A, angle BAT = 60°

To find: angle ACB

SOLUTION: As AT is tangent, and OA is radius of circle(as O is centre)

==> angle OAT = 90° [ Tangent of a circle is always perpendicular to the radius in point of contact]

As Angle BAT = 60°,

==> angle OAB= angle OAT - angle BAT

==> angle OAB= 90° - 60°

==> angle OAB = 30°

Now in ∆OAB, as OA= OB [ Radii of same circle],

==> angle OAB = angle OBA

==> angle OBA = 30°

Now in ∆OAB, using Angle Sum Property of ∆,

Angle OAB + angle OBA + angle AOB = 180°

==> 30°+30° + angle AOB = 180°

==> angle AOB = 180° - 30° -30°

==>angle AOB = 120°

Now, Reflex angle AOB = 360° - angle AOB [ Angles around a point add up to 360° ]

==> Reflex angle AOB = 360° - 120°

==> Reflex angle AOB = 240°

Thus, as angle subtended by an arc( major arc AB) at the centre is double the angle subtended by the same arc at the remaining part of the circle,

==> Reflex angle AOB = 2 × angle ACB

==> angle ACB = 1/2 × reflex angle AOB

==> angle ACB = 1/2 × 240°

==>angle ACB = 120°

THUS ANGLE ACB IS 120°

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Answer 2

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