Two circles touch each other externally as shown in the figure above. The radius of the circle with centre O is 49 cm. The radius of the circle with centre A is 16 cm. Find the length (in cm) of their common tangent BC.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 56.
The length of the common tangent BC can be found using the formula:
BC = √(OA - (OB - OC))
where OA is the distance between the centers of the circles, OB is the radius of the circle with center O, and OC is the radius of the circle with center A.
In this case, OA = 49 + 16 = 65 cm, OB = 49 cm, and OC = 16 cm. Substituting these values into the formula, we get:
BC = √(65 - (49 - 16))
BC = √(4225 - 1089)
BC = √3136
BC = 56 cm
Therefore, the length of the common tangent BC is 56 cm.