Tangential Quadrilateral Formula

Tangential Quadrilateral Formula

A convex quadrilateral with all edges tangent to a single circle within itself is known as a tangential quadrilateral in mensuration. Due to the fact that it may be drawn by encircling or circumscribing its incircles, this quadrilateral is sometimes referred to as a circumscribable quadrilateral or a circumscribing quadrilateral. The centre and radius of this circle, which is also known as the quadrilateral’s incircle or inscribed circle, are called the incenter and the inradius, respectively. The Tangential Quadrilateral Formula has been discussed below in detail for students who seek help in their studies. 

The Tangential Quadrilateral Formula must be understood by students in order for them to utilize it to respond to any inquiry. To ensure that they have a strong foundation before tackling the difficult Tangential Quadrilateral Formula, they are advised to begin their studies at the beginning of the semester. For their own benefit, students should try to fully understand the NCERT Books, since they serve as the basis of their education.

All students will benefit from the online CBSE study materials, which include the curriculum, books, sample exams, exam questions, NCERT solutions, critical thinking activities, and CBSE notes. The CBSE study guides can help Extramarks quickly prepare for their exams. Students must therefore study every day. Students will be able to do their schoolwork on time thanks to this. For the convenience of the students, a thorough explanation of the Tangential Quadrilateral Formula is provided below. This page must be read in order to comprehend the Tangential Quadrilateral Formula.

Tangential Quadrilateral

The term “tangential quadrilateral” refers to a convex quadrilateral whose sides are all tangent to the same circle. This circle’s radius is known as the inradius, and its centre is known as the incenter of the quadrilateral or its inscribed circle.

These quadrilaterals are also known as circumscribable quadrilaterals, circumscribing quadrilaterals, and circumscriptible quadrilaterals because they can be drawn encircling or circumscribing their incircles. Tangential polygons are a special case of tangential quadrilaterals.

The Tangential Quadrilateral Formula on Extramarks is a fantastic resource for exam preparation. Students may utilize the Tangential Quadrilateral Formula to better understand the various question types that may be included in the annual exam. The Tangential Quadrilateral Formula will aid students in understanding the key concepts and subjects that frequently appear on board exams. These suggestions can help students focus and respond to more test questions. To excel in Mathematics, students must be able to memorize and recall a variety of theoretical ideas. It could be challenging for students to remember all the concepts. Students sometimes forget the topics they already know when learning new ones.

Characteristics of Tangential Quadrilateral

  • The quadrilateral must contact the circle on all four sides.
  • The quadrilateral must completely enclose the circle. The circle must not extend outside of the quadrilateral in any way.
  • At the centre of the inscribed circle, the angle bisectors of the quadrilateral’s four sides converge.
  • Two opposed sides’ lengths added together must be equal. For instance, if a tangential quadrilateral has the following four sides: a, b, c, and d. And therefore, a+c equals b+d.
  • If a quadrilateral meets all of the requirements listed above, it can become a tangential quadrilateral.

Area Formula of Tangential Quadrilateral

Dimensions of a Tangential The semi-perimeter and radius of the inscribed circle can be used to calculate a quadrilateral. Consider the following hypotheses:

A, B, C, and D are four sides.

The radius of the incircle or inscribed circle is equal to r. Semi-Perimeter (Half Perimeter) or s = (a+b+c+d)/ 2

As a result, A = r.s is the quadrilateral’s area.

A= abcd is a different formula for quadrilateral area.

But be sure to confirm that a+c = b+d before you perform the calculation.

Construction of Tangential Quadrilateral

Make the angle bisector of the corner’s four angles.

At a location inside the quadrilateral, the angle bisectors will meet. The inscribed circle’s centre is referred to as this location.

Draw a circle that touches each side of the quadrilateral, starting from that location. Tangents to the circle are the sides of the quadrilateral that touch it. A tangential quadrilateral is created as a result.

The radius of the inscribed circle is the separation between the circle’s centre and its point of tangency.

Things to Remember

The Tangential Quadrilateral Formula must be used to answer each and every query. Answers to questions about the Tangential Quadrilateral Formula are essential. You can resolve any problems regarding the Tangential Quadrilateral Formula by using the NCERT solutions. Obtaining NCERT solutions is made simpler by the educational website Extramarks. To thoroughly understand the content, students must go over the Tangential Quadrilateral Formula. Students who need assistance with tangential quadrilateral problems can do it by using the Extramarks website and mobile application.

Sample Questions

For students who desire to ace their exams, practice questions on the Tangential Quadrilateral Formula will be beneficial. The Tangential Quadrilateral Formula will be easier for students to learn because they will gain a lot from frequent practice exercises. When Extramarks ask for assistance, they provide examples. Their comprehension of the fundamental concepts underlying the Tangential Quadrilateral Formula will grow as a result.

Once they have a fundamental comprehension of the Tangential Quadrilateral Formula, students will be able to reply to inquiries based on it as it is presented. Students must adhere to the detailed guidelines provided by Extramarks in order to avoid any issues when delivering responses to questions. Students who have read widely and studied diligently are capable of passing any competitive exam.

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