2. Find x and y in the figure below, with O as the centre of the circle.
O
height y cm
base x cm
Tangent R 10 cm
Hypotenuse 26 cm
Answers
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Step-by-step explanation:
In △ABC,
⇒ ∠B=90
o
[ Given ]
⇒ AB=12cm and AC=13cm [ Given ]
Here, O is center of a circle and x is a radius.
⇒ (AC)
2
=(AB)
2
+(BC)
2
[ By Pythagoras theorem ]
⇒ (13)
2
=(12)
2
+(BC)
2
⇒ 169=144+(BC)
2
⇒ (BC)
2
=25
∴ BC=5cm
Now, AB,BC and CA are tangents to the circle at P,N and M respectively.
∴ OP=ON=OM=x [ Radius of a circle ]
⇒ Area of △ABC=
2
1
×BC×AB
=
2
1
×5×12
=30cm
2
Area of △ABC= Area of △OAB+ Area of △OBC+ Area of △OCA
⇒ 30=
2
1
x×AB+
2
1
x×BC+
2
1
x×CA
⇒ 30=
2
1
x(AB+BC+CA)
⇒ x=
AB+BC+CA
2×30
⇒ x=
12+5+13
60
⇒ x=
30
60
∴ x=2cm ples like bro❤❤
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