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प्रश्न
Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if -
they touch each other internally.
उत्तर
Radius of bigger circle = 6.3 cm
and of smaller circle = 3.6 cm
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
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संबंधित प्रश्न
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.
Two parallel tangents of a circle meet a third tangent at points P and Q. Prove that PQ subtends a right angle at the centre.
Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Prove that ∠CPA = ∠DPB.
Two circles intersect at P and Q. Through P, a straight line APB is drawn to meet the circles in A and B. Through Q, a straight line is drawn to meet the circles at C and D. Prove that AC is parallel to BD.
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 figure, given below, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively.
Given that AB = 8 cm, calculate PQ.
Two circles of radii 5cm and 3cm with centres O and P touch each other internally. If the perpendicular bisector of the line segment OP meets the circumference of the larger circle at A and B, find the length of AB.
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.
