If ABCD is a cyclic quadrilateral and AB and DC are produced to meet at Q, and BC and AD are produced to meet at R, prove that QP and RP, the bisectors of the angles BQC and CRD respectively, are at right angles to each other.

Q: In the figure, QN¯¯¯¯¯¯¯¯ is the perpendicular bisector of LM¯¯¯¯¯¯¯¯¯.Which of the following can be…

A: Introduction: Congruency is a very significant property of a triangle. Two triangles are referred to…

Q: If ABCD is a cyclic quadrilateral and AB and DC are produced to meet at Q, and Bo and AD are…

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Q: Prove if a quadrilateral ABCD is cyclic, then its opposite angles are supplementary.

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: ) Prove for any quadrilateral ABCD, the following are equivalent: ) ABCD is a parallelogram; (B) AB…

A: (8) Given      In Quadrilateral ABCD                 we have AB//CD (AB parallel CD)  ,AB=CD…

Q: Given: AABC with vertices A(-6,-2), B(2,8), and C(6,-2). AB has midpoint D, BC has midpoint E, and…

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Q: Consider the following quadrilateral with diagonal AC and from which it is known that AB || CD and…

A: Given that AB∥CD , AD∥BC AC is diagonal  Now, we know that ∠A+∠B+∠C+∠D=360° ∠A+∠B=180° ∠D+∠C=180°…

Q: In a cyclic quadrilateral ABCD, prove that JAC|_ |AB||AD|+ |BC||DC| |BD| |DC||AD|+ |BC||AB|

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Q: 1. a) The perpendicular bisectors of each side of a particular quadrilateral ABCD are concur-rent…

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Q: Suppose that O is the circumcentre of AABC and points X, Y, and Z are chosen so that BC, AC, and AB…

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Q: In the figure, QN¯¯ is the perpendicular bisector of LM¯. Which of the following can be used to…

A: Option (d) is correct.

Q: In a cyclic quadrilateral ABCD, prove that |AC| |AB||AD|+ |BC||DC| |BD|¯ |DC||AD|+ |BC||AB|" (Hint:…

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Q: 1. a) Consider a regular hexagon ABCDEF as shown. Prove that AB + AC + AD + AE + AF = 3AD F B E D b)…

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Q: If R,,R, and R, be the diameters of the excircles of a AABC 3 (opposite to the vertices A, B and C…

A: Given: R1,R2,R3 are the diameters of the excircles of a ∆ABC (opposite to the vertices A,B,C…

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

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Q: Given: MT and HA intersect at B, MA  HT , and MT bisects HA. Prove: MA ≅ HT

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Q: 11. ABCD is a quadrilateral such that if sides AB and CD are extended they will meet at a right…

A: Solution: Consider the given quadrilateral ABCD and assuming line AB and CD extended and create a…

Q: In the convex quadrilaterial ABCD the diagonals are perpendicular on one another, and they are equal…

A: A convex quadilateral ABCD. Diagonals AC and BD are perpendicular to each other and equal in length.…

Q: Given: Rhombus ABCD with diagonals AC and BD intersecting at point E Complete the table to prove…

A: The rhombus is a quadrilateral with all sides equal in length. The diagonals of a rhombus are angles…

Q: 2. Suppose that T, U, and V are the points where the incircle of AABC touches the sides BC, AC, and…

A: 2) Formula Used :  Ceva's Theorem : For any ∆ABC AT , BU and CV intersect at a point O, if  ATVB…

Q: Given: AC bisects ZA and ZC Prove: AABC = AADC в B as

A: We use ASA rule to prove that given triangles are congruent. ASA states that If two angles and the…

Q: In right AABC with right ZC, AB = 17 and BC = 15. Find the length of MN if M and N are the midpoints…

A: Given a right angle triangle ∆ABC , AB=17 and BC=15 to find the length MN.

Q: e) In the given figure, AB = AC, ZADE = 35°, and ZBED = 70°, Prove that ADBE is a cyclic 35…

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Q: In the trapezoid TXYZ, TX = 5ZY. If the diagonals meet at 0, find an expression for TO in terms of…

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Q: where ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such…

A: Given:    AB = AC   <ABP = <ACP

Q: In quadrilateral EFGH, FG HE, and FG || HE. Name the postulate that could be used to prove AEHF…

A: In the given quadrilateral EFGH, FG= HE     and FG is parallel to HE FG is parallel  to HE   and…

Q: Show that there is no “AAA" congruence theorem by sketching two triangles AABC and ADEF where ZBAC =…

A: Given: We have two triangles which are∆ABC and ∆DEF, Where, ∠BAC≅∠EDF,∠ABC≅∠DEF,∠ACB≅∠DFE

Q: a. Draw any two segments, AC and BD, that bisect each other at O. Whatappears to be true of quad.…

A: a) Consider the obtained quadrilateral ABCD, Where AC and BD bisect each other at O. So the…

Q: decide whether enough information is given to prove that the triangles are congruent using the SAS…

A: The equal sides and equal angles of two triangles are shown in diagram above.

Q: Given the quadrilateral RSTU with vertices R(5, -3), 5(9, 0), 7(3, 8),and U(-l, 5). a. Show that…

A: Given; Vertices of Quadrilateral R5,-3, S9,0, T3,8, U-1,5 The distance between the vertices R and S…

Q: For ABCD, a convex quadrilateral with AB = 13 = BD, BC = CD, AD = 10 and BCD = 90°. If M is the…

A: Given: ABCD is a convex quadrilateral AB=BD=13 and BC=CD, and M is the mid point of AD and angle…

Q: In the accompanying figure, ABCD is a trapezoid in which AD|BC and AD> BC. Prove that if AB=CD, then…

A: To prove the given angle

Q: Given: ABCD is a parallelogram and AABC S ADCB. Prove: AB 1 BC.

A: ABCD is a parallelogram in which the triangles ABC and DCB are congruent. We need to prove that the…

Q: Prove that if two triangles have congruent bases, then their areas are in the same ratio as their…

A: To show that the ratio of the areas is equal to the ratio of the heights, if the two triangles have…

Q: Consider regular octagon RSTUVWXY, with each side of length 18, and the length of diagonal RU.…

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Q: Given: Quadrilateral POST is an isosceles trapezoid with OSI| PT, ER is its median. 3. If OS=2x-6,…

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Q: Let ABCD be a convex quadrilateral, and let M be the intersection of its diagonals AC and BD.…

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Q: Suppose A- B – C, D – B – F, BĠ is the bisector of LABD, and G – B – H. Prove that BH is the…

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Q: In AXYZ, mzY = 48, and mzX < mzY. Write the sides of the triangle (XY, YZ, and XZ) in order from…

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Q: ABCD is a cyclic quadrilateral and AB and DC are produced to meet at Q, and BC and AD are produced…

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Q: In the coordinate plane, quadrilateral ABCD has vertices A(-2, 3), B(4, 5), C(10, -1), and D(8, -9).…

A: The mid-point joining the points x1,y1 and x2,y2 is represented as x1+x22,y1+y22.

Q: In the given figure, PQRS is a quadrilateral in which A, C, B and D are the mid-points of PQ, QR, RS…

A: In the given figure, we connect A to C, A to D, B to C and B to D. Also draw a diagonal SQ

Q: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of…

A: Area of semi circle having diameter of a is, Aa=πa222Aa=πa28         ...(1)  Area of semi circle…

Q: Given: ABCD is a rhombus, DE DF and FC AE. Prove: AADE ACDF.

A: Given : ABCD is rhombus DE≅DFFC≅AE

Q: ABCD is a quadrilateral with AB = x, CD = 2ỷ, and AC = 33 – ỷ. Express - BD and BC in terms of x and…

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Q: Let ABCD be a cyclic quadrilateral with AB = 4, BC = 5, C'D = 6, and DA= 7. Let A1 and C, be the…

A: Let O be the point of intersection of diagonals AC and BD. Assume θ=∠AOB.Since the triangles…

Q: Suppose that A, B, C, D and A′, B′, C′, D′ (in those orders) form the vertices of convex…

A: Consider the given: Given:AB=A'B'In a parallelogram, parallel sides have equal length.In…

Q: that if P, Q, R and S form a quadrilateral, then it cannot be cyclic.

A: A quadrilateral inscribed in a circle is known as a cyclic quadrilateral. so,  if a pair of…

Q: Proof must be a paragraph proof   Thanks

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Q: 3. Let ABCD be a quadrilateral, let P be the intersection of AB and CD, and let O be the…

A: Given that ABCD is a quadrilateral. Also, given that P is the intersection of AB and CD, O is the…