If Rp and RQ are two tangents drawn from a point R to a circle with centre O, touching it at p and Q respectively, prove or is the perpendicular bisector of PQ
Answers
Answered by
2
Answer:
Step-by-step explanation:
Consider RP and RQ are two tangents drawn from a point R to a circle with centre O, touching it at P and Q respectively,
Draw a line between PQ which intersect OR at the point M
Prove that and
In
[if two tangents are drawn to a circle, from one external point, then they have equal tangent segments]
Therefore, by SSS criterion of congruence, are congruent.
So,
therefore, because, M is the point of intersection of OR and PQ
In
Therefore, by SAS criterion of congruency, are congruent.
So, PM = QM
Now,
Thus, PM=QM and
Hence, OR is the perpendicular bisector of PQ.
Attachments:
Similar questions