Let ABC be a right triangle and H be the foot of the altitude relative to the hypotenuse BC. Let also 11 and 12 be the incenters of triangles ABH and ACH. Prove that A is the excenter of triangle 11H12 relative to 1|2

Q: In the adjacent figure, ABC is a right triangle at A, such that: AB = (V17 – 1) and AC = 2V5 D (V17…

A: This question contains 4 subparts. So, according to the guidelines, the solutions of three subparts…

Q: )Let ABC be an isosceles triangle with AB-AC Let D be the foot af the A to BC. ( Prove that AD…

A: NOTE- AS WE ARE ALLOWED TO ANSWER FIRST QUESTION IN ONE SESSION SO I HAVE ANSWERED FIRST ONE FOR…

Q: Let ABC be a right triangle and H be the foot of the altitude relative to the hypotenuse BC. Let…

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Q: 22. In A ABC, D is a point on AC and E is a point on CB such that DE AB. If AD DC and DE = of AB. 3,…

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Q: Consider the points P(1, –2, –1). Q(0, –3, 0), R(1, –1,0) and let A be the area of triangle PQR.…

A: P1,-2,-1, Q0,-3,0, R1,-1,0 Here use formula  A=12x1y1z1x2y2z2x3y3z3 Use this formula here and then…

Q: 3. Find a positive angle less than 2n which is coterminal with the angle 29TT/6.

A: Given angle = 29π6

Q: In the figure alongside, two chords PQ and RS of a circle with centre O are produced to meet at T.…

A: Since, we have been given that two chords PQ and RS of a circle withcentre O are produced to meet…

Q: Must be in a paragraph proof

A: Given: ABC is a right triangle and BEDF is a square. Since, BEDF is a square with DF=x, so all of…

Q: 6. The median to the base of an isosceles triangle is the perpendicular bisector of the base.…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: 4. D and E are any two points on the sides AB and AC respectively of the triangle ABC. DG drWn…

A: Given: D and E are any two points on the sides AB and AC respectively of the triangle ABC. DG drawn…

Q: 7.In the following figure, (LF) is parallel fto BC, prove that the triangle FHC is isosceles A F L H

A: It is given that LF is parallel to BC. And ∠AFL and ∠LFH are equal (given )

Q: Let A = (-3, 2), B = (1, 0), and C = (4, 6). Prove that ABC is a right- angled triangle.

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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: Given: AC and DF bisect each other at E Prove: ADEA = AFEC D- B.

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Q: Find a formula for the area of the triangle whose vertices are 0, v, , and v2 in R?. Choose the…

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Q: Let ABC be a triangle with AB = AC. The angl meet the sides BC and CA at D and E, respectively. Let…

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Q: 2. If a line segment joins the midpoints of two sides of a triangle, then, its length is equal to…

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Q: Find the length of side KL in the figure * AJKL is isosceles with KJ = LJ. K x+3 X-1 2х- 5

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Q: Given: AB 2 BC and D is the midpoint of AC. Prove: BD bisects ZABC.

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Q: In the adjacent figure, ABC is a right triangle angled at A. • AB = 1 cm; AC= 2 cm. • R is the point…

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Q: 9. Given: E is the midpoint of AB and CD Prove: Δ4ΕC ΔΒED

A: In the given figure - E is the mid point of AB and CD. Then,AE = BECE = DE

Q: DE 12 in $ %3D DE bisects OF find the Radis. E 6.

A: Need to find r

Q: AX and DY are altitudes oftwo similar triangles AABC and ADEF. Prove that AX:DY= AB : DE.

A: To prove AX/DY=AB/DE

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: Use the Law of Sines to prove that the angle bisector of an angle in a triangle splits the side…

A: We use sine law

Q: Which of the following completes the proof? Given: Segment AC is perpendicular to segment BD Prove…

A: Let's find.

Q: GIVEN AE = CE, AB = CD, E is the midpoint of BD. PROVE AEAB = AECD C A. %23 E B.

A: Plan :  We know that, if the three sides of two triangles are congruent then the triangles are…

Q: . If M is the midpoint of the hypotenuse AB of right triangle ABC, andAM = 6, find MB and MC.

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Q: D A В Segments AD and BC intersect at point O. Prove that AC = BD, MZABC=mZBAD.

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Q: O is the center of a circle whose circumference passes through the vertices of an equilateral…

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Q: Show that the two triangles are similar. Q P and ZN INV, so ALNQ AMNP. QLN QNL MPN MNP NMP IN

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Q: Let ABC be a triangle and let P be a point inside. Let X, Y, Z be the intersections of AP, BP, CP…

A: Using Ceva's Theorem:     CXXB·BZZA·AYYC=1 ⇒CX·BZ·AY=XB·ZA·YC

Q: Given M is the midpoint of AC, W is the midpoint of AB , P is the midpoint of BC, and BP…

A: This question is based on Congruent triangles.

Q: AWXY and AABC are isosceles, with bases WY and AB respectively. If ZX and ZB are each 50° and WX =…

A: Given, Isosceles triangle WXY and ABC. WY and AB are bases Angle X= Angle B= 50° WX=BC

Q: 3. Let r be the radius of the circle inscribed in a right triangle with legs a and b and hypotenuse…

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Q: The question is in the picture. Also, there is an example of how it should look like/how it should…

A: Sketch the situation roughly Given: F, K, E are midpoints of AP, PB, PC respectively. Prove:

Q: so that AD=c1 and BD=c2. Prove using similar triangles that (CD)?=c,C2 a?=c2(c). A C1 D C2 В b.

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Q: 3.) AWXY and AABC are isosceles, with bases WY and AB respectively. If ZX and ZB are each 50° and WX…

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Q: Find a positive angle less than 2T that is coterminal with the given angle. 19T 6. CO

A: 19π6

Q: Let AABC be a triangle. Denote the altitudes at <A, <B, and <C by AD, BE and CF, correspondingly.…

A: given that                                          AD, BE and CF are altitudes H be orthocenter…

Q: ABC is a triangle inscribed in a circle. The bisector of ÐBAC cuts BC at X and the circle at Y.…

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Q: Given: MT and HA intersect at B, (MA)(HT) and MT bisects HA Prove: MT = HA Part A: Annotate the…

A: Given : MT and HA intersect at BMA || HT and Mt bisect HAto prove : MT = HAIn ∆MAB and ∆ HBT

Q: Show that p = V2/1 - cos O in an isosceles triangle that has two sides of length p, an angle of 0…

A: This question is based on application of Cosine rule.

Q: 5. Given: In rectangle ABCD, E is the midpoint of AB, Fis the midpoint of BC, Gis the midpoint of…

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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: Given C is the midpoint of AE and BD. Prove AABC = AEDC

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Q: B GIVEN: IB || ET, IS bisects EIB, EC bisects TEI. PROVE: XBIS = TEC. T

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Q: Let ABC be a triangle and let X and Y be points on AB and AC, respectively. Let AX = 6AY = 3, XB=1,…

A: Given information: ABC be a triangle and let X and Y be points on AB and AC, respectively. AX=6,…

Q: Given: AE = CB AB = CD B is the midpoint of ED Prove: AAEB =ACBD Sy E

A: To Determine:  prove that ∆AEB≅∆CBD Given: we have two figures in which we have…