Home
Class 10
MATHS
In the given diagram, PQ and RS are comm...

In the given diagram, PQ and RS are common tangents to the two circles with centres C and D. Find the length of PQ and hence area of trapexium RSDC.

A

`54 cm^(2)`

B

`64 cm^(2)`

C

`50 cm^(2)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
A
Draw CM||RS so that `squareCMSR`becomes a rectangle, Now, we have CR=2 cm, DS=7 cm and CD=13 cm
`:." "DM=DS-MS`
`=DS-CR`
`=7-2=5 cm`
In right `DeltaDMC,` by Pythagoras theorem,
`CM^(2)=CD^(2)-DM^(2)`
`=(13)^(2)-(5)^(2)=(12)^(2)`
`:." "CM=12 cm`
`implies" "RS=12 cm" "`(`because`opposite sides of rectangle are equal)
`:." "PQ=12 cm" "`(`because`length of common tangents to two circles are always same)
`=(1)/(2)xxh`(sum of parallel sides)
`=(1)/(2)xxCM(CR+DS)`
`=(1)/(2)xx12(2+7)=54 cm^(2)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|11 Videos

  • CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|32 Videos

  • ARITHMETIC PROGRESSION

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Question|5 Videos

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Short Answer Questions|10 Videos

Similar Questions

Explore conceptually related problems

In the given figure, PT is a tangent to the circle with centre O. If OT=6cm and OP=10cm, thcn find the length of tangent PT.

In the given figure, PQ, PR and ST are tangents to the same circle. If angleP= 40^(@) and angleQRT= 75^(@) , find a, b and c

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.

In the given figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of the shade region.

In the adjoining figure, A and B are the centres of two circles. If CB=17cm, EB=15cm, then find the length of common chord.

In the figure shown above, angleQ measures 70^@ , bar(PQ)cong bar(PR) , and bar(PQ) and bar(PR) are tangent to the circle with center O at points A and B . Find , in degrees , the measure of angleAOB .

In the given figure, two tangents PQ and PR are drawn to a circle with centre C from an external point P, Prove that /_ QPR = 2 /_ OQR.

In figure-3, PQ is tangent to the circle with centre at O, at the point B. if angleAOB=100^(@) , then angleABP is equal to

In the figure, PO_|_QO. The tangents to the circle with centre O at P and Q intersect at a point T. Prove that PQ and OT are right bisectors of each other.

Two tangents PQ and PR are drawn from an external point to a circle with centre O . Prove that QORP is cyclic quadrilateral.