basic doubt on circles
I got this doubt while solving following question:|
Q)There are 2 concentric circles such that the area of the outer circle is 4 times the area of the inner circle . Let A , B, C be 3 distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 sq. units then area of triangle ABC is :
by applying Pythagoras and putting the value of inner & outer radii we can get the answer , if we assume BC is also tangent to the inner circle .
Now this is only MY DOUBT : IS IT NECESSARY THAT BC IS ALSO TANGENT TO THE INNER CIRCLE , IS IT POSSIBLE THAT BC BE A SECANT TO THE INNER CIRCLE OR MAY BE NON-TOUCHING THE INNER CIRCLE.
Re: basic doubt on circles
see there is an interesting property in geometry that when the circumradius is equal to twice the inradius then the triangle is equilateral. when the triangle is equilateral then all the 3 will be tangents to the circle. so in this question the area is given 4 times and hence the Circumradius = 2* inradius. You cal also prove it by drawing a median in an equilateral triangle. so using similarity you will be able to prove it becauce in an equ. triangle everything is same( u know in short what i mean). |