Math, asked by adityababariya4, 3 months ago

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.​

Answers

Answered by amitnrw
1

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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