# Archive for category Maths

### Ultimate concept 14(binomial theorem)

Note that

For |x|<1

Now for |x|<1, we have

By using the identity and equating coefficients we can solve several problems of sequence and binomial.

### Challenge 49(permutation combination)

See ultimate concept 13

The number of ways 3 children can distribute 10 tickets

out of 15 consecutively numbered tickets among themselves

such that they get consecutive blocks of 5, 3, and 2 ticket is:

### Ultimate concept 13(solution of triangle)

Posted by akj259 in Trigonometry on September 17, 2010

From a point M inside an equilateral triangle ABC perpendiculars MP, MQ, MR are

dropped to sides BC, CA, AB respectively.

Then

Proof:

By pythagores theorem

### Ultimate concept 12(solution of triangle)

Posted by akj259 in Trigonometry on September 17, 2010

A triangle cuts off from the circum circle three circular segments.

The largest altitudes of the segments with in radius and circum radius

of the triangle has relation

Where K, L, M are the length of the largest altitudes and R, r have usual meaning.

**Proof:
**

Let O be the circum centre of the triangle. Let D be the midpoint of BC

OD=RcosA

K=(R-RcosA)

.

### Challenge 7

Posted by akj259 in Co-ordinate Geometry on September 7, 2010

P(-3,-4) is a point on circle and let circle = intersect it at Q,R. PQ and PR intersect at A and B. find slope of line AB.