PRT is a tangent whose contact point is P to the radius OP of the circle. If POQ is 106° and QRT is 90°, find QPR and PQR
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Step-by-step explanation:
As, In the figure,
OP = OQ ( radii of the same circle)
so, angle OQP = angle OQP ...... (1)
But, In ∆OPQ, by angle sum property
OPQ + POQ + QOP = 180°
OPQ + 106° + QOP = 180°
OPQ + OPQ = 180°-106° {By (1)}
2OPQ = 74°
OPQ = 37°
Now, It is given that, PRT is tangent to Circle,
hence OPR = 90°
and hence, QPR = 90°- 37°
QPR = 53°
In rt. ∆QRP, we have,
QRP = 90° and QPR = 53°
Hence, PQR = 180°- (90°+53°) = 180° - 143°
PQR= 37°.
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