Q. 55.0( 3 Votes )
Two chords AB and AC of the larger of two concentric circles touch the other circle at points P and Q respectively. Let us prove that, PQ = 1/2 BC.
Answer :
Formula used.
⇒ Mid-point theorem.
Line joining mid-point of 2 sides of triangle is half of 3rd side of triangle
⇒ Perpendicular to chord divides the chord in 2 equal parts
Solution
As AB and AC are tangents for smaller circle
And Chords for bigger circle
The perpendicular of tangents passes through centre
And radius of smaller circle act as perpendicular to chord
Perpendicular of chord divides it into equal parts
∴ P and Q are mid-points of AB and AC
Join BC to form Δ ABC
As P and Q are mid-points of AB and AC
By mid-point theorem
Line joining mid-point of 2 sides of triangle is half of 3rd side
Hence;
PQ = 1/2 BC
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