Two tangents RQ and RP are drawn from an external point R to the circle with centre O. If angle PRQ=120, then prove that OR=PR+RQ.
Answer :
We form our diagram , As :
And we know " A tangent to a circle is perpendicular to the radius at the point of tangency. "
So,
OPR = OQR = 90 ----- ( 1 )
And In OPR and OQR
OPR = OQR = 90 ( From equation 1 )
OP = OQ ( Radii of same circle )
And
OR = OR ( Common side )
Hence
OPR OQR ( By RHS CONGRUENCY )
So,
RP = RQ ---- ( 2 ) ( BY CPCT )
And
ORP = ORQ ---- ( 3 ) ( By CPCT ), So
PRQ = ORP + ORQ , Substitute PQR = 120 ( Given ) and from equation 3 , we get
ORP + ORP= 120
2 ORP = 120
ORP = 60
And
we know Cos
So,
In OPR , we get