Question of solved question

Circles of Class 10

Question
Prove that the segment joining the points of contact of two parallel tangents passes through the centre.

Frequently Asked Questions

Calculate mode of the following data

poic26

Solution:

Explanation:

pic27

Final Answer:

Mode =50.

 

A two digit number is 4 times the sum of its digits and twice

 the product of its digits.The number is - - - - - -

 

Solution:

Explanation:

Let x be the digit in the ones place and y be the digit in the tens place, resulting in the two-digit number = 10 y + x..

Given that the sum of the digits of a two-digit integer equals four,

According to the question

two-digit integer

Final Answer:

The number is 36.

 

Prove that √3 plus √5 is irrational

that √3 + √5  is irrational

Solution:

irrationa

The angle of elevation of the top of a tower from a point on the ground

which is 30m away from the foot of the tower, is 30. Find the height of the tower.

Solution:

Explanation:

Let us take the height of the tower to be AB

Let C be the point elevation which is 30m away from the foot of the tower

We know that for a given right angled triangle,

right angled triangle

 

Final Answer:

The height of the tower :  10 Root 3m

 

Prove that the product of three consecutive positive integers is divisible by 6

Solution:

Explanation:

Let us take the three consecutive positive integers as : a,a + 1,a + 2

A number when divided by 3, will have a remainder = 0 or 1 or 2

three consecutive

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 3.

Similarly, we can show that when a number is divisible by 2, we get the remainder as 0 or 1

 remainder

Clearly, 2m and 2(m+1) both are divisible by 2.

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 2.

We can say that a,a + 1,a + 2 is always divisible by 2 ,3 ,6

 

Example: 

Let us take: 3,4,5 

3 x 4 x 5 = 60 

We can see that 60 is divisible by 6

 

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