Question

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.​

Answer 1

$\bf{\underline{Question:-}}$

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

$\bf{\underline{Given:-}}$

• CD and EF are the tangents drawn at the ends of a diameter AB of A circle with centre O.

$\bf{\underline{To \:Prove:-}}$

• CD || EF

$\bf{\underline{Proof:-}}$

• CD is tangent of the circle at the point A

Therefore,

→ CD ⊥ DA

→ ∠ OAD = 90°

→ ∠ BAD = 90° -----equ(¡)

• EF is the tangent to the circle at the point B

→ EF ⊥ OB

→ ∠OBE = 90°

→ ∠ABE = 90° -----equ(¡¡)

By equ(¡) and equ(¡¡)

∠ BAD = 90° and ∠ABE = 90°

∠ BAD = ∠ABE = 90° ( alternate angle )

$\bf{\underline{Hence:-}}$

• CD || EF ( Proved)

Answer 2

Step-by-step explanation:

EXPLANATION:

AB IS A DIAMETER PQ & RS ARE THE TANGENTS DRAWN TO THE CIRCLE AT POINT A&B. OA &OB ARE THE RADIUS DRAWN AT POINT OF CONTACT

THEREFORE OA PERPENDICULAR TO PQ & OB PERPENDICULAR TO RS

ANGLE OAP ≈ANGLE OAQ≈ANGLE OBR≈ANGLE OBS =90°

IN THE FIGURE,

ANGLE OBR= ANGLE OAQ (Alternate ANGLES)

ANGLE OBS =ANGLE OAP (ALTERNATE ANGLES)

»PQ || RS