Question

Given: XY - tangent to circles k1(P) and k2(O) OX=16, PY=6 and OP=26 Find: XY

Answer 1

Answer:

the answer is XY = 24 units.

Step-by-step explanation:

Given:

XY is tangent to the circles with center P and O respectively.

OX=16 units

PY=6 units

OP=26 units

To find:

Side XY = ?

Solution:

As per given statement, the diagram of two circles and their tangent is shown in the diagram.

We need to do one construction here,

Draw a line parallel to tangent XY from P towards OX such that it meets OX at A .

Now, let us consider triangle $\triangle OAP$. It is a right angled triangle.

With sides Hypotenuse, OP = 26 units  

Perpendicular, OA = 16 -6  = 10 units

Base AP is equal to XY.

If we find the value of Base AP, the value of XY is calculated automatically.

Let us use pythagorean theorem in $\triangle OAP$:

According to pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OP^{2} = AP^{2} + OA^{2} \\\Rightarrow 26^2=XY^2+10^2\\\Rightarrow XY^2 = 676- 100\\\Rightarrow XY = \sqrt{576}\\\Rightarrow XY = 24\ units$

Hence, the answer is XY = 24 units.