Question

In ΔABC, AB = AC and BD ⊥ AC then BD² – CD² is equal to ______.

Options

• 2CD·AD

• 2CD·AC

• 2AC·BC

• 2BC·AC

Answer 1

In ΔABC, AB = AC and BD ⊥ AC then BD² – CD² is equal to 2CD·AD.

Explanation:

AB = AC

⇒ AB² = AC²

Since BD ⟂ AC and D lies on AC.

Triangles ABD and BDC are right at D. 

So, AB² = AD² + BD²

And AC² = (AD + CD)²

= AD² + 2·AD·CD + CD²

Equate AB² and AC² 

Cancel AD² 

Then rearrange to get BD² – CD² = 2·AD·CD