PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters

jaydeebest

1 year ago

Abnormal

HackyJackyli

1 year ago

THE SOLUTION TO THIS QUESTION IS ABNORMAL.
MN and PQR are two secants of the circle MQTRN and PT is a tangent....
Mathematics JAMB 1991

PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters
A. 7.3, 5.9
B. 7.7, 12.5
C. 12.5, 7.7
D. 5.9, 7.3
Correct Answer: Option C
Explanation
PQPN=PMPR=QMNR


4.812=5PR


PR = 5×124.8=504


= 12.5

PQPN=PMPT=TMNT


PT12=5PR


PT2 = 60

PT = 60−−√


= 7.746

= 7.7

flick123

3 months ago

Given:

Two secants from point P:

𝑃
𝑀
=
5
cm
PM=5 cm

𝑃
𝑁
=
12
cm
PN=12 cm

𝑃
𝑂
=
4.8
cm
PO=4.8 cm

We find:

𝑃
𝑅
PR

𝑃
𝑇
PT (tangent length)

1. Use the Secant–Secant Theorem to Find
𝑃
𝑅
PR

For two secants from the same external point:

𝑃
𝑀
×
𝑃
𝑁
=
𝑃
𝑂
×
𝑃
𝑅
PM×PN=PO×PR

Substitute values:

5
×
12
=
4.8
×
𝑃
𝑅
5×12=4.8×PR
60
=
4.8
𝑃
𝑅
60=4.8PR
𝑃
𝑅
=
60
4.8
PR=
4.8
60
​

𝑃
𝑅
=
12.5
cm
PR=12.5 cm


𝑃
𝑅
=
12.5
PR=12.5 cm

2. Use Tangent–Secant Theorem to Find
𝑃
𝑇
PT

Tangent–Secant theorem:

𝑃
𝑇
2
=
𝑃
𝑂
×
𝑃
𝑅
PT
2
=PO×PR

Substitute:

𝑃
𝑇
2
=
4.8
×
12.5
PT
2
=4.8×12.5
𝑃
𝑇
2
=
60
PT
2
=60
𝑃
𝑇
=
60
PT=
60
​

𝑃
𝑇
=
2
15
PT=2
15
​

𝑃
𝑇
≈
7.75
cm
PT≈7.75 cm
Final Answers
𝑃
𝑅
=
12.5
cm
PR=12.5 cm
​

𝑃
𝑇
=
2
15
≈
7.75
cm
PT=2
15
​

≈7.75 cm