CIRCLES 1

Given the figure below, prove that an angle inscribed in a semi –circle is a right angle.

solution

Given:

        diameter AOB

        O as centre of circle

        C is any point in the circumference

Required to prove:   

<ACB =90⁰       

Proof:      

< at centre = 2(< at circumference)

<AOB=2(<ACB) ------------    (i)

But <AOB is a straight angle

Straight angle=180⁰

Hence, <AOB = 180⁰

Now, from (i)

<ACB = 2(<ACB)

180⁰=2(<ACB)

90⁰= <ACB     [after dividing by 2 both sides]

Hence ACB = 90⁰ proved!!!

TRY THIS.......................

Given the figure below, prove that an angle inscribed in a semi –circle is a right angle.