From an external point P, two tangent segments PA and PB are drawn to a circle with center O and a radius of 5 units. The distance from P to O is 13 units. Calculate the area of quadrilatera PAOB.
Show answer & explanation
Correct answer: B
Explanation
Has been given :
Radius of circle = 5
PO = 13
According to the formula:
Length of tangent = √(PO² − r²)
Area of quadrilateral PAOB = 2 × (1/2 × OA × PA)
PA = √(13² − 5²)
= √(169 − 25)
= √144
= 12
Area of triangle OAP= 1/2 × 5 × 12= 30
Area of quadrilateral PAOB = 2 × 30 = 60