Question

Given : In a circle with centre B arc APC = arc DQE

To Prove: Chord AC chord DE

Proof : (Fill in the blanks and complete the proof.)
In triangle ABC and triangle DBE,
side AB side DB (........)
side .... side ........ (.... ....)
ZABC = DBE ( measures of congruent arcs)
triangle ABC = triangle DBE (.......)
chord AC chord DE (......)​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• In a circle C(B,r) $\arc{APC}=\arc{DQE}$

${\sf{\green{\underline{\large{To\:Prove}}}}}$

• AC=DE

${\sf{\pink{\underline{\Large{Proof}}}}}$

From A Theorm

• Equal arc of a circle subtended equal angles at centre

From this we conclude

$\angle{APC}=\angle{DQE}$

In ∆ ABC and ∆ DBE,

AB=BE (r)

BC=BD (r)

$\angle{APC}=\angle{DQE}$

$\bigtriangleup{APBC}\cong\bigtriangleup{DBE}$(SAS)

AC=DE. (Bycpct)

Additional Information

• Area of circle=πr²

Area Sector of circle=∅/360° × πr²

• perimeter of circle=2πr
• perimeter ofSector of circle=∅/360° × 2πr

Answer 2

Step-by-step explanation:

In triangle ABC and triangle DBE,

side AB side DB (radius of the circle)

side BC Side BE (radius of the same circle)

ZABC = DBE ( measures of congruent arcs)

triangle ABC = triangle DBE ( SAS TEST)

chord AC chord DE ( Corresponding sides of congruent triangles )