[tex]\huge\bold{\texttt { \green{ Question - } }}[/tex]
1. Prove that in two concentric circles , the chord of larger circle, which touches the smaller circle is bisected at the point of contact.
2. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
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Verified answer
Given:
To Prove:
Construction:
Proof:
➟ OC is perpendicular to chord
∴ OC ⟂ AB
Lets move through a theorem (you had studied in 9th ._.) that says :
So, we can say that OC bisects the chord in two equal parts.
Hence AC = BC
_______________
Given:
To Prove:
Proof: Let in circle CD and EF are two tangents at end of diameter AB.
As we know that tangent at any point of a circle is perpendicular to the radius through point of contact.
➟ CD and EF are tangents to the circle at point A and B respectively.
∴ CD ⟂ OA
➟ ∠OAD = 90° or ∠BAD = 90°......(1)
➟ ∠OBE = 90° or ∠ABE = 90°.......(2)
From equation (1) and (2) we can say that
∠BAD = ∠ABE = 90°
Also these angles are alternate interior angles.
CD || EF
Hence, Tangents are parallel to each other.