In the given figure, two concentric circles have radii 3 cm and 5 cm. Two tangents TR and TP are drawn to the circles…

CBSE Class 10 Maths PYQ · Circles · Concentric Circles · 3 Marks · March 2024 · Standard

Solve it yourself first — then press ↓ or tap Show Solution. Use ← → for previous / next question.

773 Marks · March 2024 · Standard

In the given figure, two concentric circles have radii $3$ cm and $5$ cm. Two tangents TR and TP are drawn to the circles from an external point T such that TR touches the inner circle at R and TP touches the outer circle at P. If TR = $4\sqrt{10}$ cm, then find the length of TP.

Show SolutionHide Solution↓

Join OR, OP and OT
In $\triangle ORT$,
$OT^2 = OR^2 + TR^2 = 3^2 + (4\sqrt{10})^2 = 169$
$\therefore OT = 13$ cm
In $\triangle OPT$,
$TP^2 = OT^2 - OP^2 = 13^2 - 5^2 = 144$
$\therefore TP = 12$ cm