Question

PT is a tangents at T to a circle whose centre is O and radius 20cm. A line segment intersects with circle at point M. If MP=9cm,then find PT.​

Answer 1

Given : PT is a tangents at T to a circle whose centre is O and radius 20cm

OP intersect circle at M

MP = 9 cm

To Find :  PT

Solution:

OT =  OM = Radius = 20 cm

OP = OM + MP

=> OP = 20 + 9

=> OP = 29 cm

OP² =  OT² + PT²

=> 29² = 20² + PT²

=> PT² = 29² - 20²

=> PT² = (29 + 20)(29 - 20)

=> PT² = 49 (9)

=> PT = 7(3)

=> PT = 21

PT = 21 cm

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Answer 2

$\huge \star \mid \cal \colorbox{yellow}{ANSWER}\mid \star$

$\bf \: Given : \rm \: PT \: is \: a \: tangent. \\ \rm \: Radius = 20cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \rm \: MP = 9cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bf \: To \: Find : \rm \: PT$

$\bf \: Solution : \rm \: OT = OM = Radius = 20cm \\ \rm \: OP = OM + MP \\ \rm</p><p>OP = 20 + 9 \\ \rm \ \: \: \: \: </p><p>OP = 29cm \: \: \: \: \: </p><p></p><p>$

$\: \: \: \: \rm \: OP² = PT²+PT² \\ \rm \: \: \: \: \: </p><p>29²= 20²+PT²\\ \rm \: \: \: </p><p>PT²=29²-20²\\ \rm</p><p> \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: PT²=(29+20)(29-20)\\ \rm </p><p>PT²=49(9)\\ \rm </p><p>PT²=7(3)\\ \rm </p><p>\bf PT = 21cm\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$