Two chords AB & CD of a circle intersect at point P. If AP = 4, BP = 9 and CP = 12 find CD.

For chords intersecting inside a circle, we have AP × BP = CP × DP 4 × 9 = 12× DP 36 = 12DP Dividing by 12 on both sides we get 3 = DP Now CD = CP + DP CD = 12 + 3 = 15 .......Answer

Prove that a^0 = 1

Anything raise to 0 = 1 has been accepted without proof. But we do have a way to prove this. Before that we must know that: a^m/a^n = a^(m-n) Now We have a^0 = a^(x-x) as(x-x = 0) = a^x/a^x (Using rule at the top) = 1 hence Proved

Factorize: x² +4x -3596

The standard method to factorize is to break the middle term. But there is a better way to do this. We know that to make an expression a perfect square we add (b/2a)². Here a = 1, b = 4 So (b/2a)² = (4/2(1))² = (4/2)² = 4 So we add & subtract 4. We get x² +4x + 4 -3596 - 4 = (x²+4x+4) - 3600 = (x+2)² -60² Using the rule a² - b² = (a-b)(a+b) We get = (x+2-60)(x+2+60) =(x- 58)(x+62) .......Answer