continued ..2 remaining PS Qs... detailed explanation pls

Que 5 Geo

Consider Two Right angled Triangles

POQ = QOR (Similar Triangles)

PO = OR (Radius)
OQ = OQ (Radius, common)
angle(POQ) =angle(ROQ) = 90
Therefore
PO will be = QR

Statement 1 gives the length of minor arc PQ = 4*pi

We can find the radius from the given information and by using Pythagoras Theorem we can find the length of QR.
Hence the statement is sufficient

4. Given r = 3, arc length PR = pi.

We are asked to find the angle made by the arc POR ?

circumference = 2*pi*3 = 6pi.

We know total angle made by the circle is 360 deg.

6pi = 360 deg.
pi = 360/6 = 60 deg.


5. Given PR is diameter. arc length PQ = 4*pi. OQ is perpendicular to PR.
Find QR length.

The minor arc PQ is a quadrant since PR is the diameter and OQ is perpendicular to PR.
so 4pi is 1/4th of the total circumference. arc length QR is also equal to 4*pi.

(1/4) * 2*pi*r = 4 * pi.
r = 8.
OQ = OR = 8.
QR = sqrt(8^2 + 8^2) = sqrt(128) = 11.31

Que 4 GEO

Formula used:

minor arc (PR) = minor angle(POR)/360 * circumference of the circle
Here minor arc (PR) = pi
circumference of the circle = 2*pi*3 = 6*pi
so minor angle (POR) = 360*pi/(6*pi) = 60

@niketdoshi123 and @sam2304

Thanks ...ur replies helped ... Qs were so easy
Can you guys help me with these 3 questions also please
https://www.beatthegmat.com/3-ps-qs-i-co ... 11980.html