Question

solve question no.9??

Answer 1

the value of<ABC is 100°

Answer 2

In ∆ ATO
< ATO = 40°. (given)
< OAT = 90° ( tangent is perpendicular to radius at the point of contact)

and,

<ATO + <OAT + <AOT = 180°
=> 40°+90° + <AOT = 180°
=> <AOT = 180°-130°
=>. < AOT = 50°

In ∆ ATO and ∆BTO

OA = OB ( radii of the same circle)
OT = OT ( common side)
TA= TB ( tangents from the same exterior point)
∆ ATO ≈ ∆ BTO (SSS)
therefore,
< AOT = < BOT
or , <AOB = 2<AOT
=> <AOB = 2×50°
=> <AOB = 100°