0

Guest

Courses New

Two equal circles pass through each other’s centre. If the radius of each circle is 5 cm, whtat is length of the common chord?

Two equal circles pass through each other’s centre. If the radius of each circle is 5 cm, whtat is length of the common chord?

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student


Given that ,
2 equal circles with centre A & radii AP, AB, AQ = 5 cm And circle with centre B, & radii BP, BA & BQ = 5 cm. PQ is a common chord to both the circles.

To find :length of chord PQ= ?

Since APBQ is a rhombus, as all its sides = 5 cm & one diagonal AB = 5 cm

So, triangle PAB & triangle QAB are equilateral triangles ( as all 3 sides are equal in each triangle)
Area of equilateral triangle = (√3/4) side²

=> area of triangle PAB = (√3/4)* 25 cm²

=> area of both triangles = 2* ( √3/4) *25

=> (25√3 /2 ) cm² = area of rhombus PAQB …(1)

NOW, area of rhombus = 1/2 * diagonal AB * diagonal PQ

=> 1/2 * 5 * PQ = 25√3 /2…. ( by (1) )

PQ = (25√3/2) * (2/5)

=> PQ = 5√3 cm Ans

Thanks 699-1245_main-qimg-3c0ec60be00d67c77a324ba562ded201-c.jpeg

Think You Can Provide A Better Answer ?

Other Related Questions on 8 grade science

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More