Q. 14.6( 8 Votes )

# Masum has drawn a circle with centre ‘O’ of which AB is a chord. I draw a tangent at the point B which intersect extended AO at the point T. If ∠BAT = 21°, let us write by calculating the value of ∠BTA.

Answer :

Theory.

⇒ Exterior angle is sum of opposite interior angles

⇒ if 2 sides of triangle are equal then their corresponding angles will also be equal

Solution.

In Δ AOB

AO = OB ∵ (radius of same circle )

∴ ∠OAB = ∠OBA = 21°

In Δ BOT

∠BOT = ∠OAB + ∠OBA ∵ (Exterior angle property)

= 21° + 21° = 42°

∠OBT = 90° ∵ (Radius of circle from point of contact of tangent is 90° )

∠OBT + ∠BOT + ∠BTO = 180° ∵ (Angle sum property)

90° + 42° + ∠BTO = 180°

∠BTO = 180° - 132° = 48°

∠BTO = ∠BTA = 48°

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