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ABC is a right angled triangle in which ∠C = 90°. If BC = a, AB = c, CA = b and the length of perpendicular from C to AB be p, then,
1 + 1 = ? a² b²
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1 p -
2 p² -
1 p² - None of these
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Correct Option: C
As per the given in question , we draw a figure a right angled triangle
Here , BC = a, AB = c, CA = b
| Area of ∆ ABC = | × AB × CD = | cp | ||
| 2 | 2 |
| Area of ∆ ABC = | × BC × CA = | ab | ||
| 2 | 2 |
| ∴ | cp = | ab | ||
| 2 | 2 |
⇒ cp = ab .... (i)
Again, In ∆ ABC ,
AB² = BC² + AC²
⇒ c² = a² + b²
| ⇒ |  |  | ² | = a² + b² [From equation (i)] | |
| p |
| ⇒ | = a² + b² | |
| p² |
| ⇒ | = | ||
| p² | a²b² |
| ⇒ | = | + | |||
| p² | b² | a² |
