The two circles intersect at P and Q as shown in figure. If PQ is equal to the radius of the circle with centre C2, and it is equal to 8 cm and radius of the circle with centre C1 is 5 cm, then calculate the distance between the centres (in cm ).

Question

The two circles intersect at P and Q as shown in figure. If PQ is equal to the radius of the circle with centre C2, and it is equal to 8 cm and radius of the circle with centre C1 is 5 cm, then calculate the distance between the centres (in cm ). (A) √3+4 √3 (B) 7 √3+3 (C) 3 √10 (D) √7+√3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/04b1a7a31867fb7a53de0fd5be425973-.png" /> Let A B and C1 C2 intersect at O. OC 1=√52-42=√25-16=√9 OC 2=√82-42=√64-16=√48 ∴ OC 1+ OC 2=√3+4 √3

Q. The two circles intersect at $P$ and $Q$ as shown in figure. If $PQ$ is equal to the radius of the circle with centre $C_{2}$ , and it is equal to $8 c m$ and radius of the circle with centre $C_{1}$ is $5 c m$ , then calculate the distance between the centres (in $c m$ ).

$3 + 43$

$73 + 3$

$310$

$7 + 3$

Let $A B$ and $C_{1} C_{2}$ intersect at $O$ .
$O C_{1} = 5^{2} - 4^{2} = 25 - 16 = 9$
$O C_{2} = 8^{2} - 4^{2} = 64 - 16 = 48$
$∴ O C_{1} + O C_{2} = 3 + 43$

Q. The two circles intersect at P and Q as shown in figure. If PQ is equal to the radius of the circle with centre C2​, and it is equal to 8cm and radius of the circle with centre C1​ is 5cm, then calculate the distance between the centres (in cm ).

3​+43​

73​+3

310​

7​+3​