Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

Two equal chords AB and CD of a circle when produced, intersect at point P. Prove that PB = PD.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Const: Join centre O to P. Draw Proof: We have,

AB = CD (given)

OR = OS (equal chords are equidistant from the centre)

In ORP and OSP,

OR = OS

(each 900)

and, OP = OP (common)

ORP OSP (RHS criterion)

RP = SP …..(i)

Now, AB = CD

BR = DS ……(ii)

Subtracting (ii) from (i)

RP - BR = SP - DS

PB = PD

Answered by | 04 Jun, 2014, 03:23: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
If two intersecting chords PQ and RS of a circle make equal angles with the diameter passing through their point of intersection, then prove that the chords are equal.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the angle in the minor segment is an obtuse angle.
Asked by Topperlearning User | 05 Oct, 2017, 08:15: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the given figure, equal chords AB and CD of a circle C(O, r) cut at right angles at E. If M and N are the mid points of AB and CD respectively, prove that OMEN is a square.
Asked by Topperlearning User | 18 Aug, 2017, 08:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the figure A, B and C are three points on a circle such that the angle subtended by the chords AB and AC at the centre are 120o and 80o respectively. Determine angle BAC.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
P is the centre of the circle. Prove that begin mathsize 12px style angle end styleXPZ is equal to twice the sum of begin mathsize 12px style angle end styleXZY and begin mathsize 12px style angle end styleYXZ.
Asked by Topperlearning User | 05 Oct, 2017, 08:17: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
O is the centre of the circle, find the value of x.
Asked by Topperlearning User | 05 Oct, 2017, 08:25: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
AB and AC are two equal chords of a circle whose centre is O. If OD is perpendicular to AB and OE is perpendicular to AC, prove that begin mathsize 12px style increment end styleADE is an isosceles triangle.
Asked by Topperlearning User | 18 Aug, 2017, 08:49: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
O is the centre of the circle and PQ is a diameter. If begin mathsize 12px style angle end styleROS is equal to 40o find begin mathsize 12px style angle end styleRTQ.
Asked by Topperlearning User | 05 Oct, 2017, 08:22: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
PQ and RQ are the two chords of a circle equidistant from the centre O. Prove that the diameter passing through Q bisects begin mathsize 12px style angle end stylePQR and begin mathsize 12px style angle end stylePSR.
Asked by Topperlearning User | 18 Aug, 2017, 08:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the figure, O is the centre of a circle. Prove that x + y = z.
Asked by Topperlearning User | 05 Oct, 2017, 08:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×