Question

Ab and cd are two parallel chords of a circle such that ab = 10 cm and cd = 24 cm. if the chords are on opposite sides of the centre and the distance between them is 17 cm, what is the radius of the circle? (cm = centimetres)

Answer 1

The radius of circle is 13cm

Answer 2

Answer:

here's the answer please mark as brainliest and follow me

Step-by-step explanation:

Given:

In circle C(O,r)

We have:

OP perpendicular to AB

OQ -|- CD

✓ P,O and Q are collinear

PQ=17 cm

To find: Radius

Construction: Join OA and OC

Solun:-

Let OP=x cm . Then OQ =(17-x) cm

OA=OC=r cm

Since, perpendicular drawn from the centre to a chord of a circle bisects the chord

therefore

AP=PB=5 cm and

CQ=QD =12 cm

Applying Pythagoras Theorem:-

OA²=OP²+AP² and OC²=OQ²+CQ²

$= > \: {r}^{2} = {x}^{2} + {5}^{2} ....(1) \: and \: {r}^{2} = {(17 - x)}^{2} + {12}^{2} \\ = > {x}^{2} + {5}^{2} = {(17 - x)}^{2} + {12}^{2} \: (on \: equating \: the \: values \: of \: {r}^{2} \\ = > {x}^{2} + 25 = 289 - 34x + {x}^{2} + 144 \\ = > 34x = 408 \\ = > x = 12 \: cm \\ putting \: the \: value \: ofx \: in \: (1) \\ {r}^{2} = {12}^{2} + {5}^{2} = 169 \\ r = 13 \: cm \\ \\hence \: radius \: of \: the \: circle \: is \: 13 \: cm$