Find the angle X in the Semicircle | Learn how to Solve this Tricky Geometry problem Quickly

Learn how to find the angle X in the given diagram. Solve this tricky geometry problem by using Thales's Theorem, Central Angle Theorem, and Triangle Sum Theorem.

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Find the angle X in the Semicircle | Learn how to Solve this Tricky Geometry problem Quickly

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#PythagoreanTheorem #Pythagorean #ParallelLines
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#FindtheAngleX #HowtoSolvethisTrickyGeometryProblemQuickly #IsoscelesTriangleProperty
#IsoscelesTriangle #IsoscelesTriangles #Isosceles #Triangle #Triangles #ThalesTheorem
#CongruentTriangles #CentralAngleTheorem

Olympiad Mathematics
pre math
Po Shen Loh
Learn how to find the angle X
How to Solve this Tricky Geometry problem Quickly
Exterior Angle Theorem
Alternate interior angles
premath
premaths
circle
Radius
Diameter
Radii
Isosceles triangles
Congruent Triangles
Thales's Theorem
Thales' Theorem
Central Angle Theorem
Triangle Sum Theorem

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[massimogranzotto]

Bellissimo e interessante video professore
Grazie

[murdock]

Another example showing your excellence, Sir, many thanks! You are Master of Exterior Angle and Duke of Central Angle. No one does it better. DAC = 34° → AED = x = 56°

[vara]

The figure( problem)is daunting, but the solution consists of few steps. Thank you .

[misterenter-izrz]

Angle A+angle B=x, so we are going to find the sizes of A and B. we can do this by using angle at center and circumference theorem, therefore x=(180-68)/2=112/2=56, done. A very intelligent design of puzzle.😃

[skoijlg]

Consider the triangle AEB. The sum of the angles CAB and CBA is equal to (180-68)/2=56, since they are inscribed in a circle. And the angle X is the outer corner of the triangle and is equal to the sum of two other angles not adjacent to it.

[hanswust]

Your solution leads to the demonstration that the angle formed by two chords is half of the sum of the arches they form.

Thank you!

[jjcadman]

Wonderful!! Every time I watch one of your videos, you provide an excellent tutorial for what seemed like such a complicated problem, and you do it so clearly. Thank you!

[rameshchandraray]

Suppose the angle AOD Iis 2y.Then angle COB will be 180-68-2y, i.e.112-2y. Angle AOD is a central angle on arc AD and angle ABD is a peripheral angle on the same arc. Therefore, angle ABD is y. Similarly angle CAD is 56 -y. Therefore, by exterior angle property of a triangle, for triangle BAE, x=y+56-y = 56.

[alexrocha]

Bom dia MESTRE
Agradeço ao Sr ´por ter me ensinado Geometria
Forte Abraço do Rio de Janeiro
Grato

[alster]

The Central Angle Theorem was a bit tricky; but after seeing the shaded right triangle, I knew the answer was 56°

[cotneps]

you could done that by this . we know that this is semi circle so it is 180. dc = dob so it is 68 . ad track plus cb track is 112 . ceb=ad track + bc track divided by two so 112 :2 = 56 degree

[pradeepkumar]

No need of any construction. Exterior angle X is sum of two interior angles CAO & DBO which is 56. ( apply the theorem of arc angle)

[kyongkuchang]

How about this solution.

If angle CAB is a, angle DBA is b and angle COB is c,
2a = c and 2b = 180 - (68 + c).
2a + 2b = c + 180 - 68 - c =112
So x = a + b =112/2 =56

[santiagoarosam]

∠ADB=90 ; ∠DAC=68/2=34 → En ∆ADE: ∠DEA=90-34=56 =∠CEB=X=56
Gracias y saludos cordiales.

[HappyFamilyOnline]

Great explanation👍
Thanks for sharing🌺

[hamidaqayyum]

[]《 *_Absolutely Beautiful Presentation and sharing_* 》 []
[]《 *_Greetings and Blessings from Hamida Qayyum_* 》 [] LIKE 266

[rupendrakumar]

😢😢😢 I could not make it
But ... Good... Thankyou

[harshitverma]

Degree measure theorem would have been more easy

[theoyanto]

That was cool... It looked so complicated, then pow!! Simple when you weave your magic 👍🏻🪄