Prove that the tangents drawn at the end of a diameter of circle are p

1.	Prove that the tangents drawn at the end of a diameter of circle are parallel
Answer» .Given: A circle with center O And diameter AB Let PQ be the tangent at point A & RS be the tangent at point B To prove: PQ \|\| RS Proof: Since PQ is a tangent at point A OA⟂ PQ (Tangent at any point of circle is perpendicular to the radius through point of contact) angle OAP=90°..(1) Similarly, RS is a tangent at point B OB ⟂ RS (Tangent at any point of circle is perpendicular to the radius through point of contact) angle OBS=90°....(2) From (1) & (2) angle OAP=90°& angle OBS=90°.Therefore angle OAP= angle OBS i.e. angle BAP= angle ABS For lines PQ & RS, and transversal AB angle BAP= angle ABS i.e. both alternate angles are equal So, lines are parallel : PQ II RS .... hope it would be helpful✌?

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