in each of the following figure, O is the centre of the circle find the values of x and y
Answers
Step-by-step explanation:
Consider the following question.
Using a Pythagoras theorem.
(i)AO=30cm
AB=16cm
AB=BC=y=16cm
x=BO=
(AO)
2
+(AB)
2
=
(30)
2
+(16)
2
=34cm
y=16cm
(ii)AB=12cm
BC=5cm
CA=
(AB)
2
+(BC)
2
=
(12)
2
+(5)
2
=13cm
y=
2
x
=6.5cm
(iii)AB=24cm
AO=x
OB=18cm
AO=x=
(AB)
2
+(OB)
2
=
(24)
2
+(18)
2
x=30cm
y=24cm
Answer:
X = 13, Y = 12
Step-by-step explanation:
Let 12 cm tangent be touching the circle at T
and y cm tangent be touching it at T'
we know that two tangents drawn on a circle from a same
external point p are equal
Hence length of tangents is equal
i.e. Y = 12
Now in triangle OT'P
OP is perpendicular to T'P
because tangent on a point of a circle is perpendicular to the radius on that point
we can use phythagoras theorem to find OP or x
which is given by
OP² = OT'² + T'P²
X² = 5² + 12²
X² = 25 + 144
X² = 169
X = √169
X = 13