Question

find the value of x from given circle. ​

Answer 1

Given : A circle  Tangent ST

QR || ST

∠QTS = x   and ∠QLT = x

To Find : Value of x

Solution:

ST is a  tangent

=> ∠QTL = 90° - x

∠RQT = ∠STQ    ( alternate angles  as QR || ST )

=> ∠RQT  = x  

∠RQT  = x°    , ∠RTL  = 90- x°  

Let sat QR intersects TL at  P

=> ∠QPT = 90°

Hence QP ⊥ TL

=> P is mid point of TL

=> TM = ML

in ΔQPL  and ΔQPT

=> QP = QP  common

   ∠QPL = ∠QPT = 90°

  PL = PT   as P mid point of TL

=> ΔQPL  ≅ ΔQPT

∠QLP = ∠QTP

=> x = 90° - x

=> 2x = 90°

=> x = 45°

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