P is a point at a distance 12 cm from the centre O of a circle of radius 5 cm. PA and PB are the tangents to the circle at A and B. If AB = 12 cmthen find the value of chord AB.
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Given : P is a point at a distance 12 cm from the centre O of a circle of radius 5 cm.
PA and PB are the tangents to the circle at A and B.
To find : the value of chord AB.
Solution:
OP = 12 cm
OA = OB = Radius = 5 cm
PA² = OP² - OA²
=> PA² = 12² - 5² = 119
=> PA = √119
area of ΔOAP = ΔOBP = (1/2) * 5 * √119
=> area of OAPB ( rhombus) = 2 * (1/2) * 5 * √119 = 5√119
Also area of rhombus = (1/2) * product of diagonals
one diagonal = OP = 12
another diagonal = AB
Hence = (1/2) * 12 * AB = 5√119
=> AB = 5√119/6 cm
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