tangent chord theorem

The tangent and cotangent came via a different route from the chord approach of the sine. These developed together and were not at first associated with angles. They became important for calculating heights from the length of the shadow that the object cast. The length of ..

Find the point on the parabola y = ( x + 3) 2 , at which the tangent is parallel to the chord of the parabola joining the points (- 3, 0) & (- 4, 1). => (- 4, 1) or (- 5 2 , 1 4 ) or (- 2, 1) or (- 7 2 , 1 4 )..

Find the point on the graph of f ( x ) = x 3 , at which the tangent is parallel to the chord joining the points (1, 1) & (3, 27). => ( ( 1 3 3 ) 1 2 , ( 1 3 3 ) 3 2 ) or ( 13 3 , 3 13 ) or (1, 1) or (0, 0)..

Find the point at which the tangent to the curve f ( x ) = x 2 - 6 x + 1 is parallel to the chord joining the points (1, - 4) & (3, -8). => (2, -7) or (2, 7) or (-2, -7) or (-2, 7)..

Two circles A and B have the common tangent of length ( c ) 14 cm. The external segment is of length ( a ) 10 cm for the circle A and ( b ) 12 cm for the circle B. Find the length x and y of the chords. => x = 10.60 cm, y = 5.33 cm or x = 9.60 cm, y = 4.33 cm or x = 4.33 cm, y =..

In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The derivatives also help in examining..

A line which intersects the circle at two distinct points is a => secant or diameter or tangent or chord..

Trigonometry is a fascinating tool, initially conceived from chords in a Unit-Circle it has wide applications and whenever space is involved Trigonometry is used irrespective of the area of interest. Trigonometry involves the study of concepts like the Sine, Cosine, Tangent and..

>Langrange's Mean Value theorem: If a function f (x) is such that (i) f (x) is continuous on [a,b] and (ii) f (x) is differentiable on (a,b) then Geometrical interpretation of Lagrange's Mean value theorem. Let A(a , f(a)) and B(b , f(b)) be two points on the curve y = f (x) suc..

1. If m = 0 the tangent at (x 1 , y 1 ) is parallel to x-axis. 2. If m 1 = m 2 the curves touch each other. 3. Rolle's theorem 4. Langrange's Mean Value theorem 5. Maxima and Mini..