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BQ = AQ [ tangents from same points]
BQ = 27
RB = RQ - BQ = 38 -27 = 11
CR = RB = 11
SC = RS - RC = 28 - 11= 17
Now In quadrilateral CODS
CSD = 90°
SCO = 90°
SDO = 90°
therefore
CODS IS A RECTANGLE
we know the opposite sides of a rectangule are equal
So
OD = SC
r = 17
BQ = 27
RB = RQ - BQ = 38 -27 = 11
CR = RB = 11
SC = RS - RC = 28 - 11= 17
Now In quadrilateral CODS
CSD = 90°
SCO = 90°
SDO = 90°
therefore
CODS IS A RECTANGLE
we know the opposite sides of a rectangule are equal
So
OD = SC
r = 17
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