Question

In the figure, AB is a chord of the circle and AOC is a diameter such that (triangle)ACB = 50°. If AT is the tangent to the circle at the point A, then (traingle)BAT is equal to?​

Answer 1

Answer:

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Step-by-step explanation:

now here for adjoining circle

angle acb=50 degrees (given)

so here angle acb intercepts arc ab on circumference of circle

so by inscribed angle theorem

we get

angle acb=1/2×m(arc ab)

ie m(arc ab)=50×2=100 degree

moreover here at is a tangent and ab is a secant

so here angle bat is inscribed in between both of these

so by tangent secant angle theorem

we get

angle bat=1/2×m(arc ab)

=1/2×100

=50 degrees

thus measure of angle bat is 50 degrees

OR

Here as ac is a diameter

we know that diameter subtends right angle on any point of circle ie on circumference of circle

so thus angle cba=90 degrees

so by using angle sum property on triangle abc

we get

angle cab=40 degrees

so now this then here at being a tangent

angle cat=90 degrees by tangent theorem

so thus angle bat=angle cat-angle-angle cab

=90-40

=50 degrees