The distance between the centers of two circles is d. The lengths of their direct and transverse common tangents are  L and M, respectively. If $L^2 +M^2= 200$ and the sum of the squares of their radii is 100, what is the value of d?

The distance between the centers of two circles is d. The lengths of their direct and transverse common tangents are  L and M, respectively. If $L^2 +M^2= 200$ and the sum of the squares of their radii is 100, what is the value of d?
दो वृत्तो के केंद्रों के बीच की दूरी है d. उनकी सीधी और अनुप्रस्थ उभयनिष्ठ स्पर्श रेखाओं की लंबाइयाँ क्रमश: L और M हैं। यदि $ L^2 + M^2 = 200$ और उनकी त्रिज्याओं के वर्गों का योग 100 है, तो 100 है, तो d का मान क्या है?