Question) TC is a tangent drawn to the circle with centre O. If $∠ A C S = 67 ° F i n d ∠ T A C, ∠ T O C & ∠ A O C$ .

Question

Question) TC is a tangent drawn to the circle with centre O If
∠ A C S = 67 °   F i n d   ∠ T A C ,
  ∠ T O C   &   ∠ A O C

Lovina Kansal · Accepted Answer

Dear student
Clearly,∠OCT=90°     [∵Tangent to a circle at a point is prependicular to the radius through the point of contact
]Also∠OCT+∠OCS=180°⇒∠OCS=90°Also, OA=OC⇒∠OAC=∠OCA    [Angles opposite to equal sides are equal]Also, ∠OCS=∠OCA+∠ACS⇒90°=∠OCA+67°⇒∠OCA=23°=∠OAC=∠TACIn △AOC∠OCA+∠OAC+∠AOC=180°   [Angle sum property of △]⇒23°+23°+∠AOC=180°⇒∠AOC=134°and ∠AOC+∠TOC=180°      [Linear pair]⇒∠TOC=180°-134°=46°
Regards

Question) TC is a tangent drawn to the circle with centre O. If ∠ A C S = 67 ° F i n d ∠ T A C , ∠ T O C & ∠ A O C .

Question) TC is a tangent drawn to the circle with centre O. If $∠ A C S = 67 ° F i n d ∠ T A C, ∠ T O C & ∠ A O C$ .