Ask a Doubt
Request a call back

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

CBSE Class 10 Answered

if from any point on the common chord of two intersecting circles,tangents be drawn to the circles,prove that they are equal.
Asked by | 23 Feb, 2013, 03:49: PM
answered-by-expert Expert Answer

Let the two circles intersect at points M and M. MN is the common chord.

Suppose O is a point on the common chord and OP and OQ be the tangents drawn from A to the circle.

OP is the tangent and OMN is a secant.

According to the theorem which says that if PT is a tangent to the circle from an external point P and a secant to the circle through P intersects the circle at points A and B, then  PT2 = PA × PB

Therefore, OP2 = OM*ON (1)
 
Similarly, OQ is the tangent and OMN is a secant for that also. 
Therefore OQ2 = OM*ON (2)
 
Comparing 1 and 2
 
OP2 = OQ2
i.e OP = OQ
Hence, he length of the 2 tangents is equal. Hence proved. 
Answered by | 23 Feb, 2013, 08:19: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test Subjective Questions Webinar Subjective Questions Pre Board Assessment
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
in the given figure a triangle abc is drawn to circumscribe a circle of radius 3 cm such that the segment bd and dc are respectively of length 6 and 9 cm if the area of traingle abc is 54cm2 then find side ab and ac
question image
Asked by jennyy | 26 Mar, 2022, 08:41: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
3. Two supplementary angles are subtended at the centre by two arcs of a circle of radius 7 cm. Find the total length of these arcs  
Asked by sowmyashreeiyer | 31 Jan, 2022, 11:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
From a point P, two tangents PA and PB are drawn to a circle C(0, r).  If OP = 2r, then find ∠𝐴𝑃𝐵. What type of triangle is APB?  
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
in the above figure major
question image
Asked by ajabraosable27 | 11 Oct, 2021, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
prime factorisation
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
radious of circle is
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
In the adjoining figure, AB is the Diameter of the circle. E is not the centre. Angle ACD = 30°. Find angle x.
question image
Asked by bhilarevishwesh | 21 May, 2021, 08:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Q30
question image
Asked by sangyaswarupa | 16 Mar, 2021, 10:06: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
point A lies in the exterior of a circle with center P and radius 8 cm A tangent from A touches the circle at if AB=15 cm find PA
Asked by sinhkaran79 | 14 Mar, 2021, 12:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt