Question

A circle with centre O and radius 12.5 cm passes through points P,Q and R. Seg PQ is the diameter of the circle. If l(PR)=20 cm, then l(RQ)=______.

Answer 1

Answer:

use Pythagoras theorem u will get the answer

Answer 2

$\large\underline{\sf{Given- }}$

• A circle with centre O passes through three points P, Q and R.

• PQ is diameter of circle.

• Radius of circle = 12.5 cm

• Length of PR = 20 cm

$\large\underline{\sf{To\:Find - }}$

• Length of RQ.

$\large\underline{\sf{Solution-}}$

Since, it is given that

• PQ is diameter of circle.

So,

• Length of PQ = 2 × radius = 2 × 12.5 = 25 cm.

Again,

• P, R and Q lies on circumference of circle and PQ is diameter.

So,

• ∠ PRQ = 90° [Angle in semi-circle is 90°].

Now,

• In right triangle PRQ,

We have,

• Length of PQ = 25 cm

• Length of PR = 20 cm

So,

• Using Pythagoras Theorem,

$\rm :\longmapsto\: {PR}^{2} = {PQ}^{2} + {RQ}^{2}$

$\rm :\longmapsto\: {25}^{2} = {20}^{2} + {RQ}^{2}$

$\rm :\longmapsto\:625 = 400 + {RQ}^{2}$

$\rm :\longmapsto\:625 - 400 = {RQ}^{2}$

$\rm :\longmapsto\:225 = {RQ}^{2}$

$\rm :\longmapsto\:{RQ}^{2} = {15}^{2}$

$\bf\implies \:RQ \: = \: 15 \: cm$

Additional Information :-

• 1. Perpendicular drawn from centre bisects the chord.

• 2. Equal chords are equidistant from centre.

• 3. If chords are equidistant, they are equal.

• 4. Angle subtended at the centre by an arc is double the angle subtended at the circumference.

• 5. Angle in same segments are equal.