please answer my question
Answers
Answer:
Third Option
Step-by-step explanation:
Given :-
AB = 15 cm and AC = 7.5 cm
To find :-
Find the radius of the circle ?
Solution :-
Given that
O is the centre of the circle.
AB is the tangent .
AB = 15 cm
AC = 7.5 cm
and
Radius of the circle = OB = OC = OD
Let the radius be r cm
OB = OC = OD = r cm
Join O and B
We know that
The angle between the radius and the tangent drawn from the external point to the circle at the point of contact is 90°
We have ,
∆ OAB is a right angled triangle,
OA is the hypotenuse.
By Pythagorous Theorem,
OA² = OB² + AB²
We have, OA = OC + CA
=> (OC+CA)² = OB²+AB²
=> (r+7.5)² = r²+15²
=> r²+2(r)(7.5)+(7.5)² = r²+225
Since (a+b)² = a²+2ab+b²
Where, a = r and b = 7.5
=> r²+15r+56.25 = r²+225
In cancelling r² both sides then
=> 15r+56.25 = 225
=> 15r = 225-56.25
=> 15r = 168.75
=> r = 168.75/15
=> r = 11.25 cm
Therefore, radius = 11.25 cm
Answer:-
The radius of the given circle is 11.25 cm
Used formulae:-
→ The angle between the radius and the tangent drawn from the external point to the circle at the point of contact is 90°.
Pythagoras theorem:-
" In a right angled triangle, The square of the hypotenuse is equal to the sum of the squares of the other two sides".
→ The side opposite to the right angle in a right angled triangle is its hypotenuse.
