In the given figure AB is a chord of a circle with Centre O such that AB equal to 16 cm and radius of a circle is 10 cm. Tangents at A and B intersect each other at P. Find the length of PA.
Answers
Answered by
114
draw a line from point O which intersects AB at Q and OQ is perpendicular to AB.
AQ = BQ ( Bcz a perp. from centre of the circle to a chord, divide the chord equally)
In triangle AOQ
AO^2 = AQ^2 + OQ^2
10^2 = 8^2 + OQ^2
100 = 64 + OQ^2
OQ^2 = 100 - 64
OQ = under root 36
OQ = 6 cm
in triangle OQA and triangle OAP
OQ/ OA = AQ/PA
6/10 = 4/PA
PA = 40/6
PA = 20/3
AQ = BQ ( Bcz a perp. from centre of the circle to a chord, divide the chord equally)
In triangle AOQ
AO^2 = AQ^2 + OQ^2
10^2 = 8^2 + OQ^2
100 = 64 + OQ^2
OQ^2 = 100 - 64
OQ = under root 36
OQ = 6 cm
in triangle OQA and triangle OAP
OQ/ OA = AQ/PA
6/10 = 4/PA
PA = 40/6
PA = 20/3
Answered by
21
Ab is a chord of length 16cm of a circle of radius
Step-by-step explanation:
OA =10 cm
Perpendicular from centre to the chord bisects the chord.
So
AM = MB = 8cm
Using Pythagoras Theorem in triangle AOM
So,
OM=6
Now,
Tan angle aob=4/3(LB/OL)
NOW AGAIN TANAOB=PB/OB=4/3
BY SOLVING ANSWER IS 4/3
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