Question

PO and RS is two parallel cords of a circle on the same side of the centre 0 an
radius is 10cm. If PQ = 16cm and Rs = 12cm, find the distance between the
chords,​

Answer 1

given: In circle with centre O and radius 10

cm

chord PQ || chord RS

PQ = 16 cm, RS = 12 cm

to find: distance between the two chords,

PQ and RS

construction: Draw OT perpendicular to RS such

that it intersects RS at T and PQ at

U. Draw radii OQ and OS

solution:

since OT _|_ RS and OU _|_ PQ

TR = TS = ½RS = ½(12) = 6 cm ... (i)

UP = UQ = ½PQ = ½(16) = 8 cm ... (ii)

... (perpendicular from the centre of the circle to a chord, bisects the chord)

radius OQ = radius OS = 10 cm ... (iii)

In ∆OUQ, angle OUQ = 90° (from construction)

OQ² = OU² + UQ² (Pythagorean theorem)

OU² = OQ² - UQ²

OU² = 10² - 8² ... (from ii and iii)

OU² = 100 - 64 = 36

OU = √36

OU = 6 cm ... (iv)

In ∆OTS, angle OTS = 90° (from construction)

OS² = OT² + TS² (Pythagorean theorem)

OT² = OS² - TS²

OT² = 10² - 6² ... (from i and iii)

OT² = 100 - 36 = 64

OT = √64

OT = 8 cm ... (v)

distance between the chords;

UT = OT - OU

UT = 8 - 6 ... (from iv and v)

UT = 2 cm

Hence, distance between the two chords is 2 cm.