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CBSE Class 10 Answered

A tangent to a circle is parallel to a chord. Prove that the pojnt of contact is the mid point of the arc seperated by the chord.
Asked by rushabhjain.av | 23 Jan, 2019, 08:31: AM
answered-by-expert Expert Answer
Figure shows a tangent PT making contact at T on the circle and parallel to chord AB.
 
Let us join A and T . Also join B and T. Let us draw the normal OT at T, where O is centre of circle.
 
Since AB is parallel to PT, Normal OT is perpendicular to AB . Also chord AB is bisected at C
 
It can be proved that ΔACT and ΔBCT are congruent, because both triangles are right triangle, Tc is common side and AC= BC.
 
Hence AT = BT ;
 
Since the chords AT and BT are equal, Arc length AT is equal to arc length BT.
 
Hence T is mid point of Arc ATB
Answered by Thiyagarajan K | 23 Jan, 2019, 12:30: PM

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