Home
Class 9
MATHS
In the figure, O D is perpendicula...

In the figure, `O D` is perpendicular to the chord `A B` of a circle whose centre is `Odot` If `B C` is a diameter, show that `C A=2O Ddot`

Text Solution

Verified by Experts

Since, `ODbotAB` (given) and the perpendicular drawn from the centre to a chord bisects the chord.
`therefore` D is the mid -point of AB.
Also, O is the mid -point of BC.
Now, in `Delta ABC`, D and O are mid-points of AB and BC respectively.
Therefore, `OD|\ |AC` and `OD = 1//2 AC`.
or CA =2OD (mid-point theorem).
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    NAGEEN PRAKASHAN|Exercise Exercise 10a|22 Videos

  • CIRCLE

    NAGEEN PRAKASHAN|Exercise Exercise 10b|19 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Question)|5 Videos

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise|8 Videos

Similar Questions

Explore conceptually related problems

In the Figure,OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter,show that CA=2OD

In the figure,OD is perpendicular to the chord AB of a circle whose centre is O .If BC is a diameter,show that CA=2OD

In a circle OD is perpendicular to chord AB of a circle with centre O.If BC is a diameter then the AC/OD is:

In Figure,OA and OB ar respectively perpendiculars to chords CD and EF of a circle whose centre is O. If OA=OB, prove that CE=DF.

In the given figure, O is the centre of the circle. Name all chords of the circle.

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 given figure,AB and AC are two equal chords of a circle with centre O.Show that o lies on the bisectors of /_BAC.

In the given figure, AOB is a diameter of a circle with centre O. Find tan A tan B.

In given figure, O is the centre of the circle. A chord, which is not the diameter of the circle is

In figure PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and angleCAB = 30^@ , find anglePCA