Q) Two tangents pq and qr are drawn from an external point to a circle with centre 'o'.balu said the quadrilateral ORP is a circle do you agree ? Give reason?

Q) Two tangents pq and qr are drawn from an external point to a circle with center 'o'.balu said the quadrilateral ORP is a circle do you agree ? Give reason?


sol) what is cyclic quadrilateral?
         A) The sum of either pairs( /_A  + /_C = 180 deg    or /_B + /_D 180 deg) of opposite angles of cyclic quadrilateral is 180 degrees

Given :- PQ and PR are two tangents drawn at points "Q" and "R" from an external point"P" with center"O"



Required to prove(RTP) :- QORP is a cyclic Quadrilateral

Proof :- OR _|_ PR and OQ _|_ PQ [ tangent at a point on the circle is perpendicular to the radius through point of contact]

∠ORP = 90°

∠OQP = 90°

∠ORP + ∠OQP = 180°

Hence balu said correct QOPR is a cyclic quadrilateral. 

As the sum of the opposite pairs of angle is 180°