Question

Seg qr is a chord with centre o. P is midpoint of qr. if qr is 24, op is 10. Find radius of circle

Answer 1

Answer:

2√61

Step-by-step explanation:

construction : draw set OP and OQ

solution : QR = 24

and P is the midpoint of seg QR

therefore , QP = QR/2

QP = 24/2

QP = 12

and OP = 10 - - - ( given )

also seg OP perpendicular to chord QR - - - - ( segment joining center of a circle and midpoint of a chord is perpendicular to the chord )

In ∆ OPQ

angle OPQ = 90°

therefore OQ ^2 = OP^2 + QP^2 - -(Pythagoras theorem)

OQ^2 = 10^2 + 12^2

OQ^2 = 100 + 144

OQ^2 = 244

OQ^2 = 2√61 units

therefore , the radius of circle is 2√61 unit