Question

Chord PQ Subtends poQ=60 at the center of a circle if OP=40M Find the length of PQ is cn 60
​

Answer 1

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Question

Bookmark

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT=60

o

, find ∠PRQ.

494286

expand

Medium

Solution

verified

Verified by Toppr

Given, PQ is a chord of a circle with center O.

Also, ∠QPT=60°.

Let x be the point on the tangent PT.

∠QPT+∠OPT=90

⇒∠OPT=30

0

−∠QPT=90

0

−60

0

=30

0

In ΔPOQ

∠POQ=180−(∠OPQ+∠PQO)=180−30−30=120

0

Minor arc ∠POQ=120

0

Therefore Major arc ∠POQ=360

0

−120

0

=240

0

Angle subtended by an arc at centre is double the angle subtended by it on remaining part of circle

∴∠QRP=

2

1

∠POQ=120

0

solution

Answer 2

op =oq = radius

so OPQ is an isoceles triangle

<p=<q = x

2x+60 =180

x = 60

so opq is an equilateral triangle

so length of pq = 40cm