# Q: 4        Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

To prove :

Construction: Join AC and DE.

Proof :

Let ADC = x , DOE = y and  AOD = z

So,  EOC = z (each chord subtends equal angle at centre)

AOC + DOE +AOD + EOC =

.........................................1

OA = OD  (Radii of the circle)

OAD = ODA    (angles opposite to equal sides )

OAD + ODA + AOD =

.............................................................2

Similarly,

.............................................................3

..............................................................4

ODB is exterior of triangle OAD . So,

(from  2)

.................................................................5

similarly,

OBE is exterior of triangle OCE . So,

OBE = OCE + OEC

(from  3)

.................................................................6

From 4,5,6 ;we get

BDE = BED = OEB - OED

..................................................7

In BDE ,

DBE + BDE + BED =

...................................................8

Here,  from equation 1,

...................................9

From 8 and 9,we have

## Related Chapters

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-