In the figure. PQR is a triangle with PQ = PR and RPQ=90°. Semi-circles are drawn on PQ and PR as diameters. S is any point on the semi-circle with diameter PQ. PS is produced to cut the other semi-circle at T. PQ and PR are tangents to circles PTR and PQS respectively. Prove that: 7.1 QS = PT OV PT 7.2 RV RT S V 2 R (4) (6) [10]

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In the figure. PQR is a triangle with PQ = PR and RPQ=90°. Semi-circles are drawn
on PQ and PR as diameters. S is any point on the semi-circle with diameter PQ. PS is
produced to cut the other semi-circle at T. PQ and PR are tangents to circles PTR and PQS respectively.
Prove that:
7.1 QS = PT
OV
PT
7.2
RV
RT
S
V
2
R
(4)
(6)
[10]
Transcribed Image Text:In the figure. PQR is a triangle with PQ = PR and RPQ=90°. Semi-circles are drawn on PQ and PR as diameters. S is any point on the semi-circle with diameter PQ. PS is produced to cut the other semi-circle at T. PQ and PR are tangents to circles PTR and PQS respectively. Prove that: 7.1 QS = PT OV PT 7.2 RV RT S V 2 R (4) (6) [10]
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