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Prove that a Diameter Ab of a Circle Bisects All Those Chords Which Are Parallel to the Tangent at that Point a . - Mathematics

Short Note

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at that point A .

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Solution

Consider a circle with centre at O. l is tangent that touches the circle at painted to the circle at point A. Let AB is diameter. Consider a chord CD parallel to l. AB intersects CD at point Q.

To prove the given statement, it is required to prove CQ = QD
Since l is tangent to the circle at point A.
∴  AB ⊥ l
It is given that || CD
Since CD is a chord of the circle and OA ⊥ l.
Thus, OQ bisects the chord CD.
This means AB bisects chord CD.
This means CQ = QD.
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 8 | Page 33
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