Please solve q 69?

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1 Answer
Roy Ø.
May 15, 2018

#/_BTC=44^@#

Explanation:

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The trick to solving this question is possibly to draw the line CO, which is perpendicular to TS. This will make it easier to find #/_CAB#, and, therefore #/_CBA#.

We know that #/_SCA=67^@#
Therefore #/_ACO=23^@# since #FS# is a tangent to the circle.
But as #DeltaCOA# is an isosceles triangle
#/_CAO=/_ACO=23^@#

Therefore #/_BCA=90^@-/_CAB=67^@#

#/_TBC=180^@-/_CBA=180^@-67^@=113^@#
#/_TCB=180^@-(/_SCA+/_ACB)=180^@-157^@=23^@#

Therefore #/_BTC=180^@-(/_TCB+/_BCT)=180^@-136^@=44^@#

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