Question

prove that tangents drawn at the end and diameter are parallel​

Answer 1

Answer:

.

Step-by-step explanation:

tangent to any point of cirle formed 90. degree with the line joining from point of contact to center of circle.

so, two tangent on two ends of diameter formed 90 degree each . again , by using, co interior angle property, sum of angles are 180 degree, thus two tangents are parallel , by parallel lines theorem using co interior property

Answer 2

ANSWER:

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The Diameter of circle is AB with center O.

★ Let PQ be the tangent at point A.

★ And RS be the tangent at point B.

We have to prove, PQ || RS.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

We know that,

★ Tangent at any point of a circle is perpendicular to the radius through points of contact.

Therefore,

✇ PQ is the tangent at point A.

So, OA ⊥ PQ

∴ ∠OAP = 90°$\qquad\qquad\sf ....eq.(1)$

Similarly,

✇ RS is the tangent at point B.

So, OB ⊥ RS

∴ ∠OBS = 90°$\qquad\qquad\sf ....eq.(2)$

━━━━━━━━━━━━━━━━━━━━━

✇ Now, Form eq(1) and eq(2),

• ∠OAP = 90°
• ∠OBS = 90°

L.H.S = L.H.S

Therefore,

➯ ∠OAP = ∠OBS

i.e. ∠BAP = ∠ABS

For line PQ and RS, and transversal AB.

∠BAP = ∠ABS i.e both alternate angles are equal so line are parallel.

∴ PQ || RS.