Advertisements
Advertisements
Question
Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centres if:
- they touch each other externally,
- they touch each other internally.
Solution
Radius of bigger circle = 6.3 cm
And radius of smaller circle = 3.6 cm
i.
Two circles are touching each other at P externally. O and O' are the centers of the circles. Join
OP and O'P
OP = 6.3 cm, O'P = 3.6 cm
Adding,
OP + O'P = 6.3 + 3.6 = 9.9 cm
ii.
Two circles are touching each other at P internally. O and O' are the centers of the circles. Join
OP and O'P
OP = 6.3 cm, O’P = 3.6 cm
OO’ = OP – O’P = 6.3 – 3.6 = 2.7 cm
APPEARS IN
RELATED QUESTIONS
Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.
Two circle with centres O and O' are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects angle BAC.
Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T; show that the points P, B, Q and T are concyclic.
Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angles PAQ and PBQ are supplementary.
In the given figure; ABC, AEQ and CEP are straight lines. Show that ∠APE and ∠CQE are supplementary.
Two circles intersect each other at points C and D. Their common tangent AB touches the circles at point A and B. Prove that :
∠ ADB + ∠ ACB = 180°
Two circles intersect each other at points P and Q. Secants drawn through P and Q intersect the circles at points A,B and D,C. Prove that : ∠ADC + ∠BCD = 180°
Two circles with centres O and P intersect each other at A and B as shown in following fig. Two straight lines MAN and RBQ are drawn parallel to OP.
Prove that (i) MN = 20 P (ii) MN= RQ.
P and Q are the centre of circles of radius 9 cm and 2 cm respectively; PQ = 17 cm. R is the centre of circle of radius x cm, which touches the above circles externally, given that ∠ PRQ = 90°. Write an equation in x and solve it.
Two circles with centres O and O' touch each other at point L. Prove that, a tangent through L bisects the common tangent AB of the two circles at point M.
Given: AB is a common tangent of the two circles that touch each other at point L. ML is a tangent through point L.
To prove: M is a mid-point of the tangent AB or MA = MB.
Proof: From the figure,
M is an external point that draws two tangents, MA and ML to the circle with the centre O.
So, `square` = `square` ......(i)
Similarly, M draws two tangents ML and MB to the circle with the centre O'.
So, `square` = `square` ......(ii)
From the equations (i) and (ii),
`square` = `square`
Hence, the tangent at the point L, bisects the common tangent, AB of the two circles at point M.