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# Tangents and Intersecting Chords Solutions for ICSE Board Class 10 Mathematics

Last updated date: 12th Sep 2024
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## Tangents and Intersecting Chords Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

Free download of step by step solutions for Class 10 Mathematics Chapter 18 - Tangents and Intersecting Chords of ICSE Board (Concise - Selina Publishers). All exercise questions are solved & explained by an expert teacher and as per ICSE board guidelines.

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## Tangents and Intersecting Chords Solutions

### Here are Some Theorems for Tangents and Interesting Chords for ICSE Class 10 Mathematics

Theorem 1: When two chords meet in a circle, the lengths of one chord's segments equal the lengths of the other chord's segments.

Formula of interesting chords:(segment piece) x (segment piece) =  (segment piece) x (segment piece)

Formula: a  b = c d

Theorem 2: The product of the length of one secant segment and its external portion is identical to the product of the length of the second secant segment and its external part if two secant segments are drawn to a circle from the same exterior point.

Formula of Secant: (whole secant) x (external part) = (whole secant) x (external part)

Formula: a b = c  d

Theorem 3: If a secant segment and tangent segment are drawn to a circle from the same external point, the length of the tangent segment is between the length of the secant segment and the length of the external part of the secant segment.

Formula of Secant-Tangent: rule3mOR (whole secant) x (external part) = (tangent)2

Formula: rule 3mm

## FAQs on Tangents and Intersecting Chords Solutions for ICSE Board Class 10 Mathematics

1. What is the interesting chord theorem?

The chord theorem, also known as the intersecting chords theorem, is a statement in basic geometry that states the relationship between the four-line segments formed by two intersecting chords within a circle. It states that the lengths of the line segments on each chord are equal in the product.

2. Is the converse true as well in the interesting chord theorem?

The converse is also true: if the equation above holds for two line segments AC and BD intersecting in S, then their four ends A, B, C, and D are on a common circle. In other terms, a cyclic quadrilateral is one in which the diagonals of a quadrilateral ABCD cross in S and satisfy the equation above. The absolute value of the power of S is the value of the two products in the chord theorem, which depends only on the distance of the intersection point S from the circle's center.

3. What is the Tangent - Secant theorem?

The tangent-secant theorem describes the relationship between the circle and the line segments formed by a secant and a tangent line. This solution is given in Book 3 of Euclid's Elements as Proposition 36.

The following equation holds if a secant g intersects the circle at points G1 and G2 and a tangent t intersects the circle at point T, and g and t intersect at point P:

Similar triangles can be used to show the tangent-secant theorem (see graphic).

The tangent-secant theorem, like the intersecting chords and intersecting secants theorems, is one of the three fundamental examples of the power of point theorem, which is a more general theory concerning two intersecting lines and a circle.

4. What is the Intersecting Secants Theorem?

The Intersecting Secants theorem, also known as the just secant theorem, discusses the relationship between two intersecting secants and the circle they generate.

The following equation holds for two lines AD and BC that meet in P and a circle in A and D, respectively B and C:

PA .|PD|=|PB . PC|

The intersecting secants theorem, along with the intersecting chords theorem and the tangent-secant theorem, is one of the three main examples of the power of point theorem, which is about two intersecting lines and a circle.

5. How to prepare for Tangents and Intersecting Chords for Class 10th board examination?

First of all, it is important to be thorough with the fundamentals of geometry when it comes to learning Tangents and intersecting chords. Then, it is important to be thorough with theorems like Intersecting Chord theorem, Tangent Secant Theorem, Interesting Secants Theorem and PowerPoint Theorem. Further, it can be safe to say that practice makes a man perfect. Therefore, it is very important to constantly practice the problems and find solutions to them. You can also practice sample papers. Vedantu app and website have free study materials for tangents and intersecting chords for ICSE Board Class 10 Mathematics.