Question

2. In the Fig given below, if A, B, C, D are four
points on a circle such that the chord AD
chord BC prove that the two chords AC and
8D are of equal length​

Answer 1

Given−

A,B,C&Darepointsonthecircumferenceofacircle.

AC&BDintersectatE.

AB&CDhavebeenjoined.

∠BEC=130

o

&∠ECD=20

o

.

Tofindout−

∠BAC=?

Solution−

WejoinBC.

∠DEC+∠BEC=180

o

.(linearpair)

∴∠DEC=180

o

−∠BEC=180

o

−130

o

=50

o

.

So,inΔDEC,wehave

∠CDE=180

o

−(∠DEC+∠ECD)=180

o

−(50

o

+20

o

)=110

o

.

(anglesumpropertyoftriangles)

NowthechordBCsubtends∠CDE&∠BACtothe

circumferenceofthegivencircleatD&Arespectively.

∴∠CDE=∠BAC=angle

(sincetheangles,subtendedbyachordofacircletodifferent

pointsofthecircumfereceofthesamecircle,areequal).

Ans−OptionB.