Skip to main content

Theorem 22

Theorem 2. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Given: - A circle with centre O and an arc AB subtending at the centre and on the remaining part of the circle at C.

To prove:-

Construction:- CO is joined and produced to P. OA and OB are joined

Proof:- In

OA = OC     (Radii)

[Angle opposite to equal sides]

[Exterior angle of ]

     [ ]

Similarity, by taking we have

Adding (i) and (ii) in fig (i) we have

Similarty, subtracting (i) from (ii) in fig. (ii) We have

Note: -

(i) Angle in a semi-circle is a right angle.
(ii) The circle drawn with hypotenuse of a right triangle as diameter pass through its opposite verdes or the arc of a circle subtending a right angle at any point on the remaining part of the circle is a semicircle.

 

www.cbsekey.com
Other Educational Portals
English | cbse | Science | Mathematics
Labels:

Comments

Post a Comment

Popular posts from this blog

Chivvy (Class VII - English Honeycomb - Chapter 4)

NCERT Textbook Exercise Questions (Important only) Working with the Poem Q.2: The last two lines of the poem are not prohibitions or instructions. What is the adult now asking the child to do? Do you think the poet is suggesting that this is unreasonable? Why? Ans: In the last two lines the adults are asking the child to think himself and to be independent in taking decisions in some matters. The adults are asking to be firm and determined which is unreasonable because they themselves don’t allow the child to take any decision. They always tell him what to do or what not to do. So, their asking the child to make up his own mind is totally unreasonable. Q.3: Why do you think grown-ups say the kind of things mentioned in the poem? Is it important that they teach children good manners, and how to behave in public? Ans: The grown-ups say such kind of things to their children in order to teach those good manners, etiquettes and how to behave in public. It is important to teach the children ...
30 comments
Read more

The Missing Mail | Class IX - Interact in English

NCERT / CBSE Literature Reader for English Course (Communicative) Important Exercise Questions Q.3: (a) Why is Ramanujam worried about getting his daughter married? Give four reasons. (b) How does the postman console and guide Ramanujam and his family during each of the instances you have listed in 3 (a)? Ans 3(a): Ramanujam is worried as he could not find a suitable match to marry his daughter off which was getting delayed because of different reasons. The four causes of his worriedness are - (i) Sometimes horoscopes did not match, (ii) Sometimes the girl’s appearance were not approved, (iii) At times there were problems of too much dowry and other financial matters, (iv) The season was closing with only three more auspicious dates left, whereas, he was not able to finalise any alliance by that time. Ans 3(b): First instance - When Ramanujam said that horoscopes did not agree Thanappa consoled and guided him by saying that he should not utter inauspicious words and when the God wills ...
Post a Comment
Read more