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CBSE Class 10 Answered

Prove that the line segment joining the points of contact of two parallel tangents to circle is a diameter of the circle.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Construction: Through O draw OR || BA or OR || CD as AB and CD are parallel tangents.

Proof:

OPA = 90o (radius is always perpendicular to tangent)

Since OR || BA (By construction)

OPA + POR = 180o

POR = 180o - 90o = 90O

Similarly QOR = 90o

POR + QOR = 180o

PQ is straight line through O. So PQ is diameter.

Answered by | 04 Jun, 2014, 03:23: PM

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