Question

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

Answer 1

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 l || 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.