CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics
Q. 23. In Fig. 4, AB is a chord of length 9.6 cm, of a circle with centre O and radius 6 cm. The tangents at A and B intersect at P. Find the length of PA.
Sol. Join OP. Let it intersect AB at point M.
Then 
PAB is an isosceles and PO is the angle bisector of 
APB
So, OP 
AB and therefore, OP bisects AB which gives
AM=MB=
Also OAP=900…………. 
In rt. AMO,OM=
= 
=
= 
LetPA =xcm and PM = Y cm
In rt AMP, x2 = y2 + (4.8)2 (Pythagoras’ theorem)
X2= y2 + 23.04 …(i)
In rt. ΔPAO, OP2 = PA2 + AO2
…(Pythagoras’ theorem)
(y + 3.6) 2= x2 + (6) 2
y2 + (3.6) 2 + 2(y) (3.6) = y2 + 23.04 + 36 …[From (i)]
12.96 + 7.2y = 59.04
7.2y = 59.04 – 12.96 = 46.08
From(i),x2 = y 2+23.04
=(6.4)2+23.04
=40.96+23 .04 = 64
Tangent, PA ,x =
=+8 cm
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