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QUESTION 3 3.1 In the diagram below, ABCD is a cyclic quadrilateral of the circle with centre O. Use the diagram to prove the theorem which states that ? + ? = 180°. 3.2 In the diagram TR is a chord of circle PQRST. QAT ? PAS. ? = 30°. QPS = PSR. Give a reason for each of the statement that you make when answering the following questions:

          QUESTION 3
3.1 In the diagram below, ABCD is a cyclic quadrilateral of the circle with centre O.
Use the diagram to prove the theorem which states that ? + ? = 180°.
3.2 In the diagram TR is a chord of circle PQRST. QAT ? PAS. ? = 30°. QPS = PSR.
Give a reason for each of the statement that you make when answering the following questions:

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QUESTION 3
3.1 In the diagram below, ABCD is a cyclic quadrilateral of the circle with centre O.
Use the diagram to prove the theorem which states that ? + ? = 180°.
3.2 In the diagram TR is a chord of circle PQRST. QAT ? PAS. ? = 30°. QPS = PSR.
Give a reason for each of the statement that you make when answering the following questions:

Added by Nuria A.

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Instant Answer

Solved by Expert Gaurav Kalra

06/11/2023

Step 1

1 In the diagram below, ABCD is a cyclic quadrilateral of the circle with centre 0. Use the diagram to prove the theorem which states that B+ D= 1800. Proof: Since ABCD is a cyclic quadrilateral, we know that opposite angles are supplementary. In other words, the Show more…

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QUESTION 3 3.1 In the diagram below, ABCD is a cyclic quadrilateral of the circle with centre O. Use the diagram to prove the theorem which states that Ĕ + တ = 180°. 3.2 In the diagram TR is a chord of circle PQRST. QAT ⊥ PAS. ထ = 30°. QPS = PSR. Give a reason for each of the statement that you make when answering the following questions:

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Transcript

00:01 Hi, we're given here that abcd is a cyclic quadrilateral.

00:13 Abcd is a cyclic quadrilateral and we need to prove here angle b plus angle d is equal to 180.

00:32 We need to prove here angle b plus angle d is equal to 180.

00:37 That's we have right.

00:39 Now we go for the construction here.

00:40 This construction is join a with o and c with o.

00:55 So join a with o and c with o.

01:06 That's we have here.

01:07 Alright.

01:09 So now just going to go towards the proof here.

01:14 So for the proof we have a property here.

01:22 The property is if we have a circle here and we have an arc here.

01:29 Now this arc subtends angle 2x at the center.

01:36 Then it will subtend angle x at the remaining part of circle.

01:44 This property we need to use here.

01:46 So if we take this out it will be angle x this is angle y.

01:51 Right.

01:52 And if you look at this arc here.

01:55 Now this arc subtends angle x at center and angle b at the remaining part.

02:03 So we have angle b will be x over 2...

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