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Polyhedrons

Let O A, O B,...

Question

Let be three rays such that lies between. Suppose the bisectors of ∠AOC and ∠COB are perpendicular to each other. Prove that B, O, A are collinear.

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Solution

Letand

Here,

From the figure:

Hence, B, O and A are collinear.

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Similar questions

Let be two rays and let be a ray between and such that ∠AOX > ∠XOB.

Let be the bisector of ∠AOB. Prove that ∠AOX − ∠XOB = 2∠COX.

Let be a ray and let and be two rays on the same side of , with between and . Let be the bisector of ∠AOB. Prove that ∠XOA + ∠XOB = 2∠XOC.

\to O X

be a ray and let

\to O A

\to O B

be two rays on the same side of

\to O X

\to O A

\to O X

\to O B

\to O C

be the bisector of

∠ A O B

∠ X O A + ∠ X O B = 2 ∠ X O C

Q. OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD

. O is any point in the interior of a triangle ABC. Prove that

1. AB + AC > OB + OC

2.AB + BC + CA > OA + OB + OC

3.OA + OB + OC > 1/2(AB + AC + BC)

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