in the given figure CA and CB are tangents to circle with centre O if OA =AC then AOB=?
a) 45 ° b) 90 ° c)30° d) 60°
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b) 90°
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1
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Given- O is the centre of a circle to which two tangents, CA&CB have been drawn at A&B respectively. ∠ACB=75
o
. To find out- ∠AOB=? Solution- OA&OB are radii drawn from O to A&B respectively.
∴∠OBC=90
o
=∠OAC since the radius through the point of contact of a tangent to a circle is perpendicular to the tangent. Now, considering the quadrilateral AOBC, we have ∠OBC+∠OAC+∠ACB+∠AOB=360
o
(by angle sum property of quadrilateral)
⟹90
o
+90
o
+75
o
+∠AOB=360
o
⟹∠AOB=105
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