Two tangents xy and xz are drawn from a point x to a circle with centr

Question

Two tangents xy and xz are drawn from a point x to a circle with centre w. If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

A) 65
B) 60
C) 70
D) 75

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shameekv1989 · Answer

Answer would be 65. It is based on 2 properties.

i) Tangents are perpendicular with the radius of the circle. 
ii) 2 Tangents are equal in length originating from the same point outside the circle to that circle.

Using pythagorous theorem we can form separate equations to know the length of wx (center to outside point x). yz will be cut into half by this line wx.

Answer - A

Kinshook · Answer

Hi  shameekv1989 
Please explain your solution in detail for bold portion

Kinshook · Answer

Given: Two tangents xy and xz are drawn from a point x to a circle with centre w. Asked: If the length of xz is 156 and the length yz is 120, what is the radius of the circle? Screenshot 2020-05-22 at 11.48.36 PM.png Let radius be 65. 156^2 + 65^2 = 24336 + 4225 = 28561 = 169^2 = (104+65)^2 IMO A I tried to solve this problem using quadratic equations, but could not solve it easily. Putting values of radius and verifying solutions worked well.

talwarmeister · Answer

Here is a good solution for this https://gmatclub.com/forum/two-tangents ... 25192.html

Two tangents xy and xz are drawn from a point x to a circle with centr

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