In the given figure, AB || DE and BD || EF. Prove that $DC^2$ = CF x АС

 In the given figure, AB || DE and BD || EF. Prove that $DC^2$ = CF x АС

Since $AB \parallel DE$ and $BD \parallel EF$, triangles formed by these parallel lines with transversals are similar by the basic proportionality theorem (Thales' theorem).

Using similarity properties in $\triangle DCF$ and $\triangle ACD$:

Since $\triangle DCF \sim \triangle ACD$, we have the property of similar triangles:

$ \frac{DC}{AC} = \frac{CF}{DC} $

Cross multiplying:

$ DC^2 = CF \times AC $

$\boxed{DC^2 = CF \times AC}$

• Nidhi received simple interest off Rs. 1200 when invested Rs x at 6% p.a. and Rs y at 5% p.a. for 1 year. Had she invested Rs. x at 3% p.a. and Rs. y at 8% for that year, she would have received simple interest of Rs 1,260. Find the values Rs. x an y.
• The letters A, B, C, D, E, F and G not necessarily in that order, stand for seven consecutive integers from 1 to 10, D is 3 less than A, B is the middle term. F is as much less than B as C is greater than D, G is greater than F.
• A liquid 'P' is $1\frac{3}{7}$ times as heavy as water and water is $1\frac{2}{5}$ times as heavy as another liquid 'Q' The amount of liquid ‘P' that must be added to 7 litres of the liquid ‘Q' so that the mixture may weigh as much as an equal volume of w
• A sum of Rs. 2600 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 9% per annum for 6 years. The sum lent out at 9% is
• The average of 8 numbers is 19. The average of first and sixth numbers is 17 and that of the third, fifth and seventh numbers is \(24\frac{1}{3}\). If the second number is less than the fourth number by 8, and greater than the eighth number by 2, then the

B I U OL Table

Captcha

Refresh

Submit Answer