Question

This is a question from the chapter circles of class Xth, pls help
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Answer 1

Answer:

Angle BAT = 50 degree

Step-by-step explanation:

angle ACB = angle BAT = 50 (angles in alternate segment.)

OR

Angle ABC = 90 (angle of semi-circle)

In triangle BAC

BAC + ACB + ABC = 180 (sum of all angles of triangle is 180)

BAC + 50 + 90 = 180

BAC = 40

OAT = 90 (radius of circle is perpendicular to the tangent)

BAC + BAT = 90

BAT = 50

Answer 2

Answer:

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Step-by-step explanation:

so angle acb=50 degrees

so here angle acb intercepts arc ab on circumference of circle

thus by inscribed angle theorem

we get

angle acb=1/2×m(arc ab)

ie m(arc ab)=50×2

=100 degrees

so here as ab is a chord and at being a tangent

angle bat is inscribed in between both at and ab

so by applying tangent chord theorem ie tangent secant angle theorem

we get

angle bat=1/2×m(arc ab)

=1/2×100

=50 degrees

hence angle bat=50 degrees