In a right ΔABC right-angled at C, if D is the mid-point of BC, prove that BC²=4(AD²-AC²).
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Answer:
Can be solved using Similar Triangle Proportion
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AB² = 4(AD² - AC²) proved
Step-by-step explanation:
Given: ΔABC is right - angled at C. D is the mid-point of BC.
To Prove: AB² = 4(AD² - AC²).
Proof:
In ΔABC, we know that:
AB² = AC² + BC²
= AC² + (2CD)²
= AC² + 4CD² [as BC = 2CD]
= AC² + 4(AD² - AC²) [From ΔACD right angled at C]
Hence proved. Please find attached diagram.
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