The incircle of Delta ABC touches the sides o | vedclass

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

Question

(A) Let $AP = AR = x$, $BP = BQ = y$, and $CQ = CR = z$ (tangents from an external point to a circle are equal in length).Given:$AB = x + y = 14$ $(1)

Vedclass · Accepted Answer

$AP = 5, BQ = 9, RC = 2$

Vedclass · Answer

(A) Let $AP = AR = x$, $BP = BQ = y$, and $CQ = CR = z$ (tangents from an external point to a circle are equal in length).Given:$AB = x + y = 14$ $(1)$$BC = y + z = 11$ $(2)$$CA = z + x = 7$ $(3)$Adding equations $(1)$, $(2)$, and $(3)$:$2(x + y + z) = 14 + 11 + 7 = 32$$x + y + z = 16$Now, subtracting each equation from the sum:$z = (x + y + z) - (x + y) = 16 - 14 = 2$$x = (x + y + z) - (y + z) = 16 - 11 = 5$$y = (x + y + z) - (z + x) = 16 - 7 = 9$Thus, $AP = x = 5$, $BQ = y = 9$, and $RC = z = 2$.

The incircle of $\Delta ABC$ touches the sides $\overline{AB}$, $\overline{BC}$ and $\overline{CA}$ at points $P$, $Q$ and $R$ respectively. If $AB = 14$, $BC = 11$ and $CA = 7$, find the lengths of $AP$, $BQ$ and $RC$.

Similar Questions

$A$ circle touches the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ of $\Delta ABC$ at the points $D, E, F$ respectively. If $AB=13$,$BC=12$,and $CA=5$,then $AD = \ldots$

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

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 $30^{\circ}$.

Two circles with centres $O$ and $O^{\prime}$ of radii $3\, cm$ and $4\, cm$,respectively,intersect at two points $P$ and $Q$ such that $OP$ and $O^{\prime}P$ are tangents to the two circles. Find the length of the common chord $PQ$ (in $cm$).

In $\Delta ABC$,$\angle B = 90^{\circ}$. The radius of the incircle touching all three sides of the triangle is $\ldots \ldots \ldots \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module