Question

if in two circle arc of the same length of stand angle 60 degree and 75 degree at the centre find the ratio of their radii.​

Answer 1

❥︎❥︎ANSWER࿐☃️✨

ʟᴇᴛ ʀᴀᴅɪɪ ᴏғ ᴄɪʀᴄʟᴇ ʀ1 ᴀɴᴅ ʀ2.

ᴛʜᴇɴ ᴀɴɢʟᴇ sᴜʙsᴛᴇɴᴇᴅ ʙʏ ᴀɴ ᴀʀᴄ ᴀᴛ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ғɪʀsᴛ ᴄɪʀᴄʟᴇ ɪs

θ = 60° = π /3 ʀᴀᴅɪᴀɴ

ᴀɴɢʟᴇ sᴜʙᴛᴇɴᴅᴇᴅ ʙʏ ᴀɴ ᴀʀᴄ ᴀᴛ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ sᴇᴄᴏɴᴅ ᴄɪʀᴄʟᴇ ɪs

= 75° = 75π /180 = 5π /12

ғʀᴏᴍ ғᴏʀᴍᴜʟᴀ :

ʟᴇɴɢᴛʜ ᴏғ ᴀʀᴄ ( ʟ ) = ʀᴀᴅɪᴜs (ʀ) x ᴀɴɢʟᴇ (θ)

∴ ʟᴇɴɢᴛʜ ᴏғ ᴀʀᴄ ᴏғ ғɪʀsᴛ ᴄɪʀᴄʟᴇ = π /3 x ʀ1 ʟᴇɴɢᴛʜ ᴏғ ᴀʀᴄ ᴏғ sᴇᴄᴏɴᴅ ᴄɪʀᴄʟᴇ = 5π /12 x ʀ2

ɢɪᴠᴇɴ ᴛʜᴀᴛ: ᴀʀᴄs ᴏғ ᴛᴡᴏ ᴄɪʀᴄʟᴇs ᴀʀᴇ ᴏғ sᴀᴍᴇ ʟᴇɴɢᴛʜ

Then,

$\frac{\pi}{3} \times r1 = \frac{5\pi}{12} \times r2$

or,

$\frac{r1}{r2} = \frac{5 \times 3}{12} = \frac{5}{4}$

r1 :r2 = 5:4

Hence the radius of the circle are r1: r2 = 5: 4.

Answer 2

Step-by-step explanation:

༒☬Aɴsᴡᴇʀ☬༒

༒Let r1 and r2 be the radii of the two circles and let their arcs of same length S subtend angles of 60° and 75° at their centres. ∴ r1 : r2 = 5 : 4.༒

༒☬ᴘᴀᴘᴀᴋᴀғɪɢʜᴛᴇʀᴘʟᴀɴᴇ☬༒