Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q $⊥$ AT. Then AO : AO' =

(a) 3/2

(b) 2

(c) 3

(d) 1/4

Open in App

Solution

From the given figure we have,

AO = r + r + r

AO = 3r

AO’ = r

Therefore,

Also as therefore

Therefore, option (c) is correct.

Suggest Corrections

Similar questions

Q. In Fig. 7, two equal circles, with centres O and O', touch each other at X. OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular AC.

Find the value of

\frac{D O^{'}}{C O}

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O' D is perpendicular to AC. Find the value of $\frac{D O^{'}}{C O}$

Q. Equal circles with centre O and O' touch each other at X. OO' produced to meet a circle with centre O, at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of

\frac{D O^{'}}{C O} .

Q. In the figure, two equal circles, with centres

O

and

O^{'}

, touch each other at

X . O^{'} X

produced meets the circle with centre

O

A . A C

is tangent to the circle with centre

O,

at the point

C .

O^{'} D

is perpendicular to

A C .

Find the value of

\frac{D O^{'}}{C O}

In fig., circles C(O,r) and $C (O^{'}, \frac{r}{2})$ touch internally at a point A and AB is a chord of the circle C (O,r) intersecting $C (O^{'}, \frac{r}{2})$ at C. Prove that AC = CB. [3 MARKS]

Join BYJU'S Learning Program

Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q ⊥ AT. Then AO : AO' = (a) 3/2 (b) 2 (c) 3 (d) 1/4

From the given figure we have, AO = r + r + r AO = 3r AO’ = r Therefore, Also as therefore Therefore, option (c) is correct.

Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q $⊥$ AT. Then AO : AO' =

(a) 3/2

(b) 2

(c) 3

(d) 1/4

From the given figure we have,

AO = r + r + r

AO = 3r

AO’ = r

Therefore,

Also as therefore

Therefore, option (c) is correct.