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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