Question

A
In the adjoining figure, three circles
with centres P, Q and Rare drawn,
such that the circles with centres Q
and R touch each other externally and
they touch the circle with centre P,
internally. If PQ = 10 cm, PR = 8 cm
and QR = 12 cm, then the diameter of
Р
R
the largest circle is​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

Any straight line segment that goes through the centre of the circle and whose endpoints are on the circle is called a diameter of a circle in geometry.

Given:

1. The centres Q and R touch each other externally and they touch the circle with centre P, internally.

2. PQ = 10 cm, PR = 8 cm and QR = 12 cm.

Find:

The diameter of P and R.

Solution:

Let the radius of three circles with centres P, Q, and R be p, q, and r.

From the diagram given below,

$p=8+r=10+q$           ...... eq (1)

( ∵ p is the radius of the circle with centre P.)

Also, $r=12-q$

Put this value in eq (1)

$8+12-q=10+q\\20-10=2q\\q=5cm$

$r=12-q\\r=12-5\\r=7cm$

Put values of r and q in eq (1) to get the value of p

$p=8+r\\p=8+7\\p=15cm$

∵ Diameter of the circle = 2×Radius of the circle

The diameter of P $=2*15=30cm$

The diameter of R $=2*7=14cm$

∴ The largest circle is P with a diameter of 30 cm.