If PA and PB are tangents from an external point P to a circle with centre O such that ∠APB=70∘, find ∠AOB
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Step-by-Step Solution
Step 1: Identify properties of tangents and radii
We know that the radius drawn to the tangent at the point of contact is perpendicular to the tangent. Therefore, the angle between the radius OA and tangent PA is 90∘, and similarly, the angle between radius OB and tangent PB is 90∘.
Step 2: Apply angle sum property of quadrilateral
The sum of the interior angles of any quadrilateral is 360∘. In the quadrilateral OAPB, we have four angles: ∠OAP, ∠APB, ∠OBP, and ∠AOB.
Step 3: Substitute known values and solve for ∠ AOB
Substitute the known values into the equation: ∠OAP=90∘, ∠APB=70∘, and ∠OBP=90∘. Then, solve for ∠AOB by subtracting the sum of the known angles from 360∘.