Question

Please explain it on level of class 10

Answer 1

What is Tangent secant theorem:

⇒ It states that if a tangent and secant drawn from an external point to a circle, then the square of the measure of the tangent is equal to product of secant external part and entire secant.

Step-by-step explanation:

From figure:

Given: AB = AC   ----- (i)

AD = (1/2) AC   ----- (ii)

By applying Tangent secant theorem, we get

⇒ AE * AB = AD²

⇒ AE = (AD)²/AB

⇒ AE = (AC/2)²/AB

⇒ AE = A²C²/4AB

⇒ AE = A²C²/4AC

⇒ AE = (1/4)AC

Hope it helps!

Answer 2

Hey Mate...

AD is a tangent and AB is a secant

So, we will prove this sum by tangent-secant theorem.

According to theorem "When a tangent and secant are drawn from one single external point to a circle, square of the length of the tangent segment must be equal to the product of lengths of whole secant segment and exterior portion of secant segment"

Therefore, by tangent-secant theorem:

AD^2 = AE*AB
AE=AD^2/AB
AE=(AC/2)^2/AB
Because D is mid point
AE=AC^2/4AB
Now, AB=AC
So, AE=AC^2/4AC
AE=1/4AC

---HENCE PROOVED---