Question

AB is a diameter of a circle with centre O.
CB is a tangent to the circle at B. AC
intersects the circle at G. If the radius of
the circle is 6 cm and AG = 8 cm, then
the length of BC is:
केन्द्र 0 वाले वृत्त का एक व्यास AB है। बिन्दु B पर,
वृत्त पर CB एक स्पर्श रेखा है। AC वृत्त को G बिन्दु
पर काटता है। यदि वृत्त की त्रिज्या 6 सेमी. और AG =
8 सेमी. है, तो BC की लंबाई हैं:
(A) 245 cm (B) 6-6 cm
___(C) 216 cm (D)615 cm
11:11​

Answer 1

BC = 6√5 cm    AB is a diameter of a circle with centre O. CB is a tangent to the circle at BAC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm

Step-by-step explanation:

AC²  = AB²  + BC²

=> AC²  = 12²  +  BC²

BG² = AB² - AG²

=> BG²  = 12² - 8²

=> BG² = 80

BG² + GC² =  BC²

80 + GC² = BC²

AC²  = 12²  +  BC²

=> (AG + GC)²  = 12²  +  80 + GC²

=> ( 8 + GC)² = 144 + 80 + GC²

=> 64 + GC² + 16GC =  224 + GC²

=> 16GC = 160

=> GC = 10

80 + GC² = BC²

=> 80 + 10²  = BC²

=> 180  = BC²

=> BC = 6√5

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