In ⊙P, QR≅ST. Which statement must be true? Select all that apply.

A circle with center point P and four points Q,R,S,T on the circumference. Line segments join the points to make three chords QR,RS and ST. All the four points are connected to center point P making three triangles QPR,RPS and SPT.
A. △QRP ≅ △STP
B. QR¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
C. ∠QPS ≅ ∠RPT
D. △RPS ≅ △SPT
E. QR¯¯¯¯¯¯¯¯ ≅ ST¯¯¯¯¯¯¯Which is the length of PQ expressed in terms of π?

A circle with center point N and radius 1. It has a minor arc PQ whose angle measures 99 degree

A. 1140π
B. 2940π
C. 1120π
D. 2920π

Question

17-05-2022
Mathematics

contestada

In ⊙P, QR≅ST. Which statement must be true? Select all that apply.

A circle with center point P and four points Q,R,S,T on the circumference. Line segments join the points to make three chords QR,RS and ST. All the four points are connected to center point P making three triangles QPR,RPS and SPT.
A. △QRP ≅ △STP
B. QR¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
C. ∠QPS ≅ ∠RPT
D. △RPS ≅ △SPT
E. QR¯¯¯¯¯¯¯¯ ≅ ST¯¯¯¯¯¯¯Which is the length of PQ expressed in terms of π?

A circle with center point N and radius 1. It has a minor arc PQ whose angle measures 99 degree

A. 1140π
B. 2940π
C. 1120π
D. 2920π

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MrRoyal MrRoyal · Answer 1 · 2022-05-18T12:39:47+02:00

The true statement about the circle with center P is that triangles QRP and STP are congruent, and the length of the minor arc is 11/20π

The circle with center P

Given that the circle has a center P

It means that lengths PQ, PR, PS and PT

From the question, we understand that QR = ST.

This implies that triangles QRP and STP are congruent.

i.e. △QRP ≅ △STP is true

The length of the minor arc

The given parameters are:

Angle, Ф = 99

Radius, r = 1

The length of the arc is:

L = Ф/360 * 2πr

So, we have:

L = 99/360 * 2π * 1

Evaluate

L = 198/360π

Divide

L = 11/20π

Hence, the length of the minor arc is 11/20π