Draw a circle and two lines parallel to a given line such that one is tangent and other a secant to the circle.

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Solution

$G i v e n - O i s t h e c e n t r e o f a c i r c l e . P T i s a t a n g e n t t o t h e g i v e n c i r c l e . A C i s a s e c a n t t o t h e g i v e n c i r c l e . P T ∥ A C . T o d r a w - t h e c i r c l e w i t h P T a s a t a n g e n t a n d A C a s a s e c a n t . C o n s t r u c t i o n - A c i r c l e w i t h c e n t r e O i s d r a w n . A t a n g e n t P T t o t h e c i r c l e f r o m a p o i n t P, o u t s i d e t h e c i r c l e, i s d r a w n . I t t o u c h e s t h e c i r c l e a t T . W e j o i n O T . W e t a k e a n y p o i n t Q o n O T a n d d r a w a l i n e A C ∥ P T t h r o u g h Q . A C i n t e r s e c t s t h e c i r c l e a t B & C . S o P T i s t h e r e q u i r e d t a n g e n t t o t h e c i r c l e a t T a n d A C i s t h e r e q u i r e d s e c a n t t o t h e c i r c l e .$

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Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

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Q. Question 4
Draw a circle and two parallel lines such that one is a tangent and the other, a secant to the circle.

Q. Question 4
Draw a circle and two parallel lines such that one is a tangent and the other, a secant to the circle.

At most two tangents can be drawn parallel to a given secant because there are only two points on a circle through which the lines parallel to the secant are tangents to the circle.

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