Question

Anyone solve this question.?????​

Answer 1

I HOPE THIS IS CORRECT

Answer 2

Answer:

To solve this question, we need to use Pythagoras theorem and we know that we need a right angled triangle to use the theorem.

Hence, first join DB. now, the ΔADB is a right angled triangle.

( We know that angle subtended by diameter in a semi circle is a right angled triangle).

Since, ∠ADB = 90° , hence, ∠BDC =90°

Therefore, ΔBDC is also right angled at ∠BDC.

Now, in ΔADB,  AD² + BD² = AB²

and in ΔBDC, BD² + CD² = BC²

or, AB² - AD² + CD² = BC²

or, AD² - CD² + BC² = AB²

or, ( AD + CD) * ( AD - CD)  + BC² = AB²

or,  AC * ( AD - CD) + AC² - AB² = AB²

(Δ ABC is a right angled Δ, right angled at B. Therefore,  AB² + BC² = AC²)

Now,  AC * ( AD - CD) + AC² = 2 AB²

or,  AC ( AD - CD + AC) = 2 AB²

or, AC ( AD + AD) = 2 AB² (  Since, AD + CD = AC)

or, 2. AC. AD = 2 AB²

or, AC.AD = AB²

or, AC. AD = (2.radius)²

or, AC. AD = 4. radius²

Hence proved.