Two tangents are drawn to a circle from an external point $A$ , touching the circle at the points $P$ and $Q$ . A third tangent intersects segment $A P$ at $B$ and segment $A Q$ at $C$ and touches the circle at $R$ . If $A Q = 10$ units, then the perimeter of $Δ A B C$ is

22.0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20.5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

40.0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $20.0$
Since the tangents to a circle from an external point are equal in length
$A P = A Q = 10$ units
and $BP = BRCQ=CR$
Adding these, we get,
$B P + C Q = B R + C R = B C$
Adding AB and AC to both sides, we get
$B P + C Q + A B + A C = B C + A B + A C$
$\Rightarrow (B P + A B) + (C Q + A C) = A B + B C + A C$
$\Rightarrow A P + A Q = P e r i m e t e r o f$ \Delta ABC$
$\Rightarrow (10 + 10)$ units = Perimeter of $Δ A B C$
$∴$ Perimeter of $Δ A B C = 20$ units,

Suggest Corrections

Similar questions

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor PQ to intersect AP at B and AQ at C, find the perimeter of the $Δ A B C$ .

Q. From an external point P, two tangents are drawn that touches the circle at points Q and R. Then triangle PQR is a/an triangle.

In the given figure, a circle touches the side BC of Δ A B C at P. AR and AQ are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of Δ A B C (in cm) .

Q. Question 14
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q . If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

Q. In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

Join BYJU'S Learning Program

Two tangents are drawn to a circle from an external point A, touching the circle at the points P and Q. A third tangent intersects segment AP at B and segment AQ at C and touches the circle at R. If AQ=10 units, then the perimeter of ΔABC is

Two tangents are drawn to a circle from an external point $A$ , touching the circle at the points $P$ and $Q$ . A third tangent intersects segment $A P$ at $B$ and segment $A Q$ at $C$ and touches the circle at $R$ . If $A Q = 10$ units, then the perimeter of $Δ A B C$ is