27. AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents are
and B intersect at a point P. Find the length of PA.[CBSE 2010]
Answers
Answered by
3
Answer:
Join OA
OA=10cm
OL is perpendicular to AB
AL=LB=216=8cm since AL and LB are the radii of the circle.
By pythagoras theorem, in △OLA
OL2+LA2=OA2
⇒OL2=OA2−LA2
⇒OL2=102−82
⇒OL2=100−64=36
∴OL=6cm
tan∠AOL=OLAL=68=34
From △OAP
tan∠AOL=OAPA
⇒34=10PA
⇒PA=310cm
∴ Length of PA=3
Step-by-step explanation:
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Answered by
1
Answer:
Join OA
OA=10cm
OL is perpendicular to AB
AL=LB=
2
16
=8cm since AL and LB are the radii of the circle.
By pythagoras theorem, in △OLA
OL
2
+LA
2
=OA
2
⇒OL
2
=OA
2
−LA
2
⇒OL
2
=10
2
−8
2
⇒OL
2
=100−64=36
∴OL=6cm
tan∠AOL=
OL
AL
=
6
8
=
3
4
From △OAP
tan∠AOL=
OA
PA
⇒
3
4
=
10
PA
⇒PA=
3
10
cm
∴ Length of PA=
3
10
≈3.33cm
Step-by-step explanation:
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