Suppose S_1 and S_2 are two unequal circles,A | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $R$ be a point on the direct common tangent $AB$ and $S$ be a point on the direct common tangent $CD$. The transverse common tangent $PQ$ inte

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Let $R$ be a point on the direct common tangent $AB$ and $S$ be a point on the direct common tangent $CD$. The transverse common tangent $PQ$ intersects $AB$ at $R$ and $CD$ at $S$.From point $R$,the tangents to the circle $S_2$ are $RA$ and $RQ$. Since tangents from an external point to a circle are equal in length,we have $RA = RQ$.Similarly,from point $S$,the tangents to the circle $S_2$ are $SP$ and $SD$. Thus,$SP = SD$.Also,from point $R$,the tangents to the circle $S_1$ are $RA$ and $RP$. Thus,$RA = RP$.From point $S$,the tangents to the circle $S_1$ are $SC$ and $SP$. Thus,$SC = SP$.We know that $AB$ is the length of the direct common tangent. Since $R$ lies on $AB$,$AB = AR + RB$. Since $RA = RQ$,we have $AB = RQ + RB$.For the transverse tangent segment $RS$,we have $RS = RP + PQ + QS$ is not correct; rather,$R$ and $S$ are points on the direct tangents. The length of the segment $RS$ of the transverse tangent between the two direct tangents is equal to the length of the direct tangent segment $AB$ (or $CD$).Therefore,$RS = AB = 10$.

Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ Two circles,one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ Two branches of a hyperbola	$(s)$ do not have a common normal

Suppose $S_1$ and $S_2$ are two unequal circles,$AB$ and $CD$ are the direct common tangents to these circles. $A$ transverse common tangent $PQ$ cuts $AB$ in $R$ and $CD$ in $S$. If $AB=10$,then $RS$ is

Similar Questions

The radius of any circle touching the lines $3x - 4y + 5 = 0$ and $6x - 8y - 9 = 0$ is

If $A\left(\frac{\pi}{3}\right)$ and $B\left(\frac{\pi}{6}\right)$ are points on a circle represented in parametric form with center $(0,0)$ and radius $12$,then the length of the chord $AB$ is:

The length of the chord intercepted by the circle $x^2+y^2-4x+6y-12=0$ on the line $4x+3y+1=0$ is

If a circle $S$ passing through the origin and having its centre on the line $x-y=0$ cuts the circle $x^2+y^2-4x-6y+10=0$ orthogonally,then the diameter of $S$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module