6. (15 pts) Given is point P in the exterior of a circle. From P, a segment is drawn that is tangent to the circle at a point T, and a secant from P intersects the circle at points A and B. Point K is constructed on PÅ so that PK = PT. Then TK is constructed, intersecting the circle at X. All is shown below. Prove that AX = XB. X B A K P [Hint: angle and arc chase.] T
6. (15 pts) Given is point P in the exterior of a circle. From P, a segment is drawn that is tangent to the circle at a point T, and a secant from P intersects the circle at points A and B. Point K is constructed on PÅ so that PK = PT. Then TK is constructed, intersecting the circle at X. All is shown below. Prove that AX = XB. X B A K P [Hint: angle and arc chase.] T
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 41E
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![6. (15 pts) Given is point P in the exterior of a circle. From P, a segment is drawn that
is tangent to the circle at a point T, and a secant from P intersects the circle at points
A and B. Point K is constructed on PÅ so that PK = PT. Then TK is constructed,
intersecting the circle at X. All is shown below. Prove that AX = XB.
X
B
A
K
P
[Hint: angle and arc chase.]
T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322742eb-4a31-4e3c-832a-7268262542b0%2Fc766f832-5885-4261-b80f-87fddb2558a4%2Fdn0uq29_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. (15 pts) Given is point P in the exterior of a circle. From P, a segment is drawn that
is tangent to the circle at a point T, and a secant from P intersects the circle at points
A and B. Point K is constructed on PÅ so that PK = PT. Then TK is constructed,
intersecting the circle at X. All is shown below. Prove that AX = XB.
X
B
A
K
P
[Hint: angle and arc chase.]
T
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