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E4004. Tangent and Chord Problem. Tangent & Chord Problem. The points T & A lie on a tangent of circular curve TBC. ABC is a straight line. Given the noted dimensions. 81°36’20”. A. T. 20.03221. Determine the radius of the curve passing through T, B and C. B. 151°25’43” 75.26498. C.

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E4004

E4004

Tangent and Chord Problem


Tangent chord problem
Tangent & Chord Problem

The points T & A lie on a tangent of circular curve TBC

ABC is a straight line

Given the noted dimensions

81°36’20”

A

T

20.03221

Determine the radius of the curve passing through T, B and C

B

151°25’43”

75.26498

C


Tangent chord problem1
Tangent & Chord Problem

Construct OT, OA, OB and OC

Let X be the midpoint of BC and construct OX

81°36’20”

A

T

20.03221

B

151°25’43”

75.26498

X

C

O


DAXO

DCXO

DATO

From (ii)

From (iii)

81°36’20”

A

T

20.03221

B

151°25’43”

75.26498

R

X

C

O

R


DAXO

DCXO

DATO

From (ii)

From (iii)

From (i)


81°36’20”

A

T

20.03221

B

151°25’43”

75.26498

R

X

C

O

R


Close TAXOT

TA 81°36’20” 43.69226

AX 151°25’43” 20.03221+(75.26498/2)

XO 241°25’43” ( )

OT 351°36’20” ( ) = Radius

67.73889

77.49040

81°36’20”

A

43.69226

T

20.03221

B

151°25’43”

75.26498

R

X

C

O

R


CHECK

OT = OB = OC = R

Close OTABC

OT 351°36’20” 77.49040

TA 81°36’20” 43.69226

AB 151°25’43” 20.03221

MBrg = Radius

32°22’27”.277.49043

BC 151°25’43” 75.26498

MBrg = Radius

81°36’20”

A

43.69226

90°28’59”.1

T

20.03221

B

77.49052

151°25’43”

75.26498

R

X

77.49040

C

O

R