A is a point at a distance 13, cm from the ce | vedclass

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

Question

(A) Given: Two tangents are drawn from an external point $A$ to the circle with centre $O$.$OA = 13\, cm$,radius $OP = OQ = 5\, cm$.Tangent $BC$ is dr

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(A) Given: Two tangents are drawn from an external point $A$ to the circle with centre $O$.$OA = 13\, cm$,radius $OP = OQ = 5\, cm$.Tangent $BC$ is drawn at a point $R$ on the minor arc $PQ$.To find: Perimeter of $	riangle ABC$.Proof: $\angle OPA = 90^{\circ}$ [Tangent at any point of a circle is perpendicular to the radius through the point of contact].In right-angled $	riangle OPA$,by Pythagoras theorem:$OA^2 = OP^2 + PA^2$$(13)^2 = 5^2 + PA^2$$169 = 25 + PA^2$$PA^2 = 144$$PA = 12\, cm$.Since tangents from an external point to a circle are equal in length,$AP = AQ = 12\, cm$.Also,$BP = BR$ and $CR = CQ$ (tangents from points $B$ and $C$ respectively).Perimeter of $	riangle ABC = AB + BC + CA$$= AB + (BR + RC) + CA$$= AB + BP + CQ + CA$$= (AB + BP) + (CQ + CA)$$= AP + AQ$$= 12 + 12 = 24\, cm$.

Similar Questions

$\overline{PA}$ and $\overline{PB}$ are the tangents to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $m \angle APB = 70^\circ$,then $m \angle POB = \dots$ (in $^\circ$)

If $ABCD$ is a cyclic quadrilateral and $m \angle B = 60^{\circ}$,then the measure of $\angle D = \dots$ (in $^{\circ}$)

Write 'True' or 'False' and give reasons for your answer.
In the figure,$BOA$ is a diameter of a circle and the tangent at a point $P$ meets $BA$ extended at $T$. If $\angle PBO = 30^{\circ}$,then $\angle PTA$ is equal to $30^{\circ}$.

Let $P$ be the centre of a circle and $AB$ be a line in the same plane. If $Q$ is the foot of the perpendicular drawn from $P$ to the line $AB$,and $Q$ lies in the interior of the circle,then the line $AB$ ..... .

Point $P$ lies in the exterior of a circle with centre $O$. $OP = 34$ and a tangent through $P$ touches the circle at $Q$. If $PQ = 16$,then find the diameter of the circle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module