Two circles touching internally prove that ox:oy=oa:ob, Mathematics

Assignment Help:

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB.

Given : Two circles touching internally

at ‘O' . The line OXY touches the circles
at X and Y . The line OAB passes through
the centres of the circles.
R. T. P.: OX : OY = OA : OB
Construction: Join AX and BY.
Proof : OA is the diametre of the inner
circle.
∠OXA = 900 ( Angle in semicircle )......................( i )
OB is the diameter of the outer circle.

∠OYB = 900 ( Angle in the semi circle...................( ii )

From ( i ) and ( ii ); ∠OXA = ∠OYB =900

i.e., The corresponding angles are equal.
 AX // BY
In ΔOBY; AX //BY
OX/OY = OA/OB

i.e., OX : OY = OA : OB

614_circles.png


Related Discussions:- Two circles touching internally prove that ox:oy=oa:ob

Cardioids and limacons - polar coordinates, Cardioids and Limacons Thes...

Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel

Limit, limit x APProaches infinity (1+1/x)x=e

limit x APProaches infinity (1+1/x)x=e

Differential Equations, Find the normalized differential equation which has...

Find the normalized differential equation which has { x, xe^x } as its fundamental set

Chp 8 Study, Center and Radius 1)(x+2)^2-(y-3)^2=4

Center and Radius 1)(x+2)^2-(y-3)^2=4

Control a liner interpolation between original mesh, Use your keyboard to c...

Use your keyboard to control a linear interpolation between the original mesh and its planar target shape a. Each vertex vi has its original 3D coordinates pi and 2D coordinates

Naming fractions greater than 1, the 10 miles assigned to the chess club st...

the 10 miles assigned to the chess club start at the 10 mile point and go to the 20 mile point when the chess club members have cleaned 5/8 of their 10 mile section between which m

Fundamental sets of solutions, The time has at last come to describe "nice ...

The time has at last come to describe "nice enough". We've been using this term during the last few sections to explain those solutions which could be used to form a general soluti

How many cubic centimetres of cork dust will be required?, A cylindrical ve...

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between two vessels is fi

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd