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CBSE Class 10 Answered

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Asked by gpnkumar0 | 25 Feb, 2018, 09:59: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style Tangents space from space an space external space point space to space straight a space circle space are space equal.
rightwards double arrow TP equals TQ
rightwards double arrow TPQ space is space an space isosceles space triangle.
rightwards double arrow angle TPQ equals angle TQP
In space triangle space TPQ comma
angle TPQ plus angle TQP plus angle PTQ equals 180 degree
rightwards double arrow 2 angle TPQ equals 180 degree minus angle PTQ
rightwards double arrow angle TPQ equals 90 degree minus fraction numerator angle PTQ over denominator 2 end fraction
rightwards double arrow fraction numerator angle PTQ over denominator 2 end fraction equals 90 degree minus angle TPQ space space space space space.... left parenthesis straight i right parenthesis
Now comma space OP perpendicular TP
rightwards double arrow angle OPT equals 90 degree
rightwards double arrow angle OPQ plus angle TPQ equals 90 degree
rightwards double arrow angle OPQ equals 90 degree minus angle TPQ space space space space space space.... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
fraction numerator angle PTQ over denominator 2 end fraction equals angle OPQ
rightwards double arrow angle PTQ equals 2 angle OPQ
end style
Answered by Rashmi Khot | 26 Feb, 2018, 10:53: AM
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