Question

Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. Find measure angle APB.​

Answer 1

Answer:

Step-by-step explanation:Given X and Y are two circles touch each other externally at P. AB is the common tangent to the circles X and Y at point A and B respectively.

let ∠CAP=α and ∠CBP=β.

CA = CP [lengths of the tangents from an external point C].

In a triangle PAC, ∠CAP=∠APC=α

Similarly CB = CP and ∠CPB=∠PBC=β

Now in the triangle APB,

∠PAB+∠PBA+∠APB=180  

 [sum of the interior angles in a triangle]

α+β+(α+β)=180  

 2α+2β=180  

 α+β=90

 Thereofre, ∠APB=α+β=90