two circles with centre at A and B, and of radius 5 cm and 3 cm touch Each Other internally. if the perpendicular bisector of segment AB meets a bigger circle in P and Q, find the length of PQ.
Answers
Answer:
So, in figure we can see that AC is radius of bigger circle and BC is radius of circle.
As in given question
AC = 5 cm and BC = 3 cm
AC - BC = AB
5 cm - 3 cm = AB
2 cm = AB
Now, PQ is perpendicular bisector of AB so AD = 1 cm.
Now, since ∆ADP is right triangle at D so,
AP² = PD² + AD²
5² - 1² = PD²
√24 = PD
2√6 cm = PD
Now, PQ is chord which intersect AC that passes through centre so AC is perpendicular bisector on PQ.
PD = QD
PD + QD = PQ
2PD = PQ
2(2√6) = PQ
4√6 = PQ.
Hence length of PQ is 4√6.
Answer:
The (a - b)3 formula is also known as one of the important algebraic identities. It is read as a minus b whole cube. Its (a - b)3 formula is expressed as (a - b)3 = a3 - 3a2b + 3ab2 - b3How To Simplify Numbers Using the (a - b)3 Formula?
Let us understand the use of the (a - b)3 formula with the help of the following example.
Example: Find the value of (20 - 5)3 using the (a - b)3 formula.
To find: (20 - 5)3
Let us assume that a = 20 and b = 5.
We will substitute these in the formula of (a - b)3.
(a - b)3 = a3 - 3a2b + 3ab2 - b3
(20-5)3 = 203 - 3(20)2(5) + 3(20)(5)2 - 53
= 8000 - 6000 + 1500 - 125
= 3375
Answer: (20 - 5)3 = 3375.