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R.D. Sharma Class 6 Solutions | Maths Chapter 2 Playing With Numbers Exercise

Solution Video Solution. Tangent at any point of a circle is perpendicular to the radius through the point of contact. Hence the correct Option is A. Hence the correct Option is B. SSS congruence rule: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

If two triangles are congruent then their corrresponding pars are equal. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. What is known? We know that, according to Theorem Hence, it is proved that Tangents drawn at the ends of a diameter of a circle are parallel.

Prove that the perpendicular at the point of contact to class 10 maths ch 2 ex 2.4 cell tangent to a circle passes through the center. Perpendicular at the point of contact to the tangent to a circle class 10 maths ch 2 ex 2.4 cell through the centre.

Reasoning and Steps:. By theorem, tangent at any point of a circle is perpendicular to the radius through the point of contact. What is Known? The length of the chord of the larger circle which touches the smaller circle.

SSS Congruence Rule: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points class 10 maths ch 2 ex 2.4 cell contact at the center. The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the point of contact at the center.

According to Theorem Therefore, opposite sides are equal. Hence other sides can be calculated. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle. Opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle. Steps and Reasoning:. We know that, tangents drawn from an external point to a circle subtend equal angles at the center.

Tangents drawn from an external point to a circle subtend equal angles at the centre. Class 10 Maths Solutions. Book a Free Class. Exercise Chapter 10 Ex. Ncert Class 10 Exercise Related Sections. Instant doubt clearing with Cuemath Advanced Math Program.

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Then carry out the division process. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes. No login or registration is required to access any content. Download Exercise 2. Class 10 Maths Exercise 2. Find the sum and product of its other two zeroes. Find g x. Find the total number of trees planted by both students.

How do we start division of a polynomial by another polynomial? A real number is said to be a zero of a polynomial. Remainder theorem: To understand the remainder theorem, we must have knowledge about factors and multiples, long division algorithms.

If f x is any polynomial of a degree 1 and f x is divided by the linear polynomial x � a, then the remainder is f a. Factor theorem: Sometimes a polynomial having values that are unknown and one of its factors are provided and we have to calculate the value of that unknown value. Sometimes, a linear polynomial is given and we have to verify whether it is a factor of given polynomial f x of degree greater than 1 or not.

For solving such types of problems factor theorem is required. In this segment, we will study division algorithms for polynomials. If any two polynomials like p x and g x along with one polynomial of the two is not equal to 0 i. The outcome of the above numerical is known as the Division Algorithm for polynomials.

In other words, we can say that when p x divided by g x , we get q x as quotient and r x as remainder. Organize the terms of the dividend and the divisor in descending order of their degrees. The first term of the dividend must be divided by the first term of the divisor to obtain the first term of the quotient. Multiply the whole divisor by the first term if the quotient and subtract the result obtained from the dividend.

Observe the remainder as the new dividend and proceed as earlier. Repeat the procedure till a remainder is derived which is either 0 or whose degree is less than that of the divisor. Verifying the division algorithm for polynomials. Let us consider the following example. To find the Quotient and Remainder using a division algorithm.

By division algorithm, we have. Equating the quotients of various powers of x on both sides, we get. To check whether a given polynomial is a factor of the other polynomial by applying a division algorithm.

To find the remaining zeroes of a polynomial when some of its zeroes are given. Vedantu makes Mathematics interesting for even those students who are scared even by the name of the subject. Highly qualified and experienced teachers have curated the contents of the solution.

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