Mathematics - Circle Question with Solution | TestHub

MathematicsCircleCommon tangents to two circlesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q63-65: S1: x² + y² - 2x = 0 and S2: x² + y² + 6x = 0. Their two direct common tangents touch S1 at A, B and S2 at C, D; they meet at P and cut a transverse common tangent at Q, R respectively.

$S_{1} : x^{2} + y^{2} - 2 x = 0, S_{2} : x^{2} + y^{2} + 6 x = 0$ . Their two direct common tangents touch $S_{1}$ at $A, B, S_{2}$ at $C, D$ , meet at $P$ , and cut a transverse common tangent at $Q, R$ respectively. Find the incentre of $△ PC D$ .

Options:

Answer:

Solution:

The transverse tangent is $x = 0$ and $P = (3, 0)$ ; symmetry gives an equilateral $△ PC D$ whose incentre is $(0, 0)$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Common tangents to two circles

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...