State the theorem which is used …
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- State the theorem which is used for deviding a line segment in given ratio.
- In a circle chord CD is parallel to the tangent at a point A prove that angel ACD is isosceles.
Posted by Vinod Sharma 7 years, 2 months ago
- 2 answers
Naveen Sharma 7 years, 2 months ago
Ans. 1) Section Formula : The Co-ordinates of the point P(x,y) which divides the line joining the point Internally in the Ration m:n is given by .
2. Given : Chord CD is parallel to Tangent FAE.
To Prove : Triangle ACD is Isosceles.
Proof :
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Ashita Singh 7 years, 2 months ago
Construction-From center O draw a straight line connecting point of contact A on tangent to a point M on chorday
Proof-since angle between radius and tangent at point of contact is 90 thus angle formed between radius and tangent at A is 90
Now chord//tangent
Thus angle OMD is also 90
This proves that OM is perpendicular to chord
A perpendicular from centre to chord bisects the chord
Thus CM=DMITRY
IN TRIANGLE ACM AND ADM
CM=DMITRY
angleAMC=AND
AM=AM
THUS TRIANGLE ACM AND ADM ARE CONGURENT thus AC=AD
AS TWO SIDES ARE EQUAL TRIANGLE ACD IS ISOSCELES
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