$In the figure given below, O is the center of the circle, CA is tangent at A and CB is tangent at B drawn to the circle.$

$If ∠ A C B = 75^{\circ}, then find the value of ∠ A O B$ .

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Solution

$∠ O A C = ∠ O B C = 90^{\circ}$
$(∵ The tangent at any point on a circle$
$is perpendicular to the radius through$ $that point.)$

$∠ O A C + ∠ O B C + ∠ A C B + ∠ A O B = 360^{\circ}$
$(∵ Sum of angles of a quadrilateral)$

$90^{\circ} + 90^{\circ} + 75^{\circ} + ∠ A O B = 360^{\circ}$

$∠ A O B = 360^{\circ} - 255^{\circ} = 105^{\circ}$
$∠ A O B = 105^{\circ}$

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In the figure given below, O is the center of the circle, CA istangent at A and CB is tangent at B drawn to the circle. If ∠ ACB=75∘, then find the value of ∠AOB .

∠OAC=∠OBC=90∘​ (∵The tangent at any point on a circle is perpendicular to the radius throughthat point.) ∠OAC+∠OBC+∠ACB+∠AOB=360∘​ (∵Sum of angles of a quadrilateral) 90∘+90∘+75∘+∠AOB=360∘ ∠AOB=360∘−255∘=105∘​​ ∠AOB=105∘

$In the figure given below, O is the center of the circle, CA is tangent at A and CB is tangent at B drawn to the circle.$

$If ∠ A C B = 75^{\circ}, then find the value of ∠ A O B$ .