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Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.
i) The value of x is-
ii) The value of y is ----
iii) cos (A + B + C + D) =
iv) sin(B + D) =
v) cos A + cos B + cos C + cos D =?
i) The value of x is-
ii) The value of y is ----
iii) cos (A + B + C + D) =
iv) sin(B + D) =
v) cos A + cos B + cos C + cos D =?
Most Upvoted Answer
Case study 1: A quadrilateral ABCD is inscribed in a circle as shown i...
Value of x:
Given that AB is the diameter of the circle, angle ABC is a right angle. Therefore, angle ABC = 90°.
Since angle ADC is an inscribed angle, it subtends the same arc as angle ABC. So, angle ADC = angle ABC = 90°.
In quadrilateral ABCD, the sum of the opposite angles is 180°. So, angle BCD = 180° - angle ABC - angle ADC = 180° - 90° - 90° = 0°.
Since angle BCD is 0°, angle BCD is a straight angle. This implies that AD is a diameter of the circle, and angle ACD is a right angle.
Therefore, angle ACD = 90°, and angle ACD = angle A + angle D = 90°. Since angle A + angle D = 90°, we have x + y = 90°.
Given x + y = 90°, and x = 70°, we can solve for y. Therefore, y = 90° - x = 90° - 70° = 20°.
Value of y:
From the above calculations, we have already determined that y = 20°.
cos(A + B + C + D):
Since the sum of the angles in a quadrilateral is 360°, A + B + C + D = 360°.
Therefore, cos(360°) = cos(0°) = 1.
sin(B + D):
Since angle BCD is 0°, angle B + angle D = 180° (supplementary angles).
Therefore, sin(180°) = sin(0°) = 0.
cos A + cos B + cos C + cos D:
From the given quadrilateral ABCD inscribed in a circle, we have angles A, B, C, and D.
Using the cosine formula for the angles in a circle, we can calculate the cosine of each angle and sum them up.
cos A + cos B + cos C + cos D = cos(70°) + cos(90°) + cos(70°) + cos(90°)
= cos(70°) + 0 + cos(70°) + 0
= 2 * cos(70°)
Given that AB is the diameter of the circle, angle ABC is a right angle. Therefore, angle ABC = 90°.
Since angle ADC is an inscribed angle, it subtends the same arc as angle ABC. So, angle ADC = angle ABC = 90°.
In quadrilateral ABCD, the sum of the opposite angles is 180°. So, angle BCD = 180° - angle ABC - angle ADC = 180° - 90° - 90° = 0°.
Since angle BCD is 0°, angle BCD is a straight angle. This implies that AD is a diameter of the circle, and angle ACD is a right angle.
Therefore, angle ACD = 90°, and angle ACD = angle A + angle D = 90°. Since angle A + angle D = 90°, we have x + y = 90°.
Given x + y = 90°, and x = 70°, we can solve for y. Therefore, y = 90° - x = 90° - 70° = 20°.
Value of y:
From the above calculations, we have already determined that y = 20°.
cos(A + B + C + D):
Since the sum of the angles in a quadrilateral is 360°, A + B + C + D = 360°.
Therefore, cos(360°) = cos(0°) = 1.
sin(B + D):
Since angle BCD is 0°, angle B + angle D = 180° (supplementary angles).
Therefore, sin(180°) = sin(0°) = 0.
cos A + cos B + cos C + cos D:
From the given quadrilateral ABCD inscribed in a circle, we have angles A, B, C, and D.
Using the cosine formula for the angles in a circle, we can calculate the cosine of each angle and sum them up.
cos A + cos B + cos C + cos D = cos(70°) + cos(90°) + cos(70°) + cos(90°)
= cos(70°) + 0 + cos(70°) + 0
= 2 * cos(70°)
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Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =?
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Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =?.
Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =?.
Solutions for Case study 1: A quadrilateral ABCD is inscribed in a circle as shown in the figure: Based on the above data, answer any four of the following questions.i) The value of x is-ii) The value of y is ----iii) cos (A + B + C + D) =iv) sin(B + D) =v) cos A + cos B + cos C + cos D =? in English & in Hindi are available as part of our courses for JEE.
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