Question

The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs which are congruent to arc PS

Answer 1

Hi ,

It is given that ,

Diameters PQ and RS of the circle with center

C are perpendicular to each other at C.

Join P , Q to R and S shown in the picture.

Now ,

In ∆PCS , ∆QCS

CP = CQ ( radius )

CS = CS ( common side )

<PCS = <QCS = 90°

Therefore ,

∆PCS congruent to ∆QCS

( side , angle , side congruency )

PS = SQ [ corresponding parts of congruent

triangles ]

arc PS congruent arc SQ

[ If the angles subtended by two chords

at the center are equal , then the chords

are congruent. ]

And

arc PQ = arc SQ = arc QR = arc RP

all arc arc congruent to each other.

I hope this helps you.

: )

Answer 2

Step-by-step explanation:

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