Two circles of radii 20 cm and 5 cm, respectively, touch each other externally at the point P. AB is the direct common tangent of those two circles of centres R and S, respectively. The length of AB is equal
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 20 cm
| Understanding | Application |
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The length of the common tangent of two circles when they are touching each other = √(d2 – (r1 – r2)2) Where 'd' is the distance between two centers and r1, r2 are the radii of two circles. |
The length of tangent = √((20 + 5)2 – (20 – 5)2) ⇒ √((25)2 – (15)2) ⇒ √((25 + 15)(25 - 15)) ⇒ √(40 × 10) ⇒ 20 cm |