Class X Session 2023-24 Question 23

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

SECTION B - Question 23

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of ∆PCD..

Explanation:

Given an external point 𝑃 from which two tangents 𝑃𝐴  and 𝑃𝐵 are drawn to a circle with center 𝑂, we know the following:

𝑃𝐴 = 10 cm

PB=10 cm (since the tangents drawn from an external point to a circle are equal)

\[\ Perimeter \;of\; ΔPCD = PC + CD + PD \]

\[\Rightarrow PC + CE + ED + PD \]

\[\Rightarrow PC + CA + DB + PD \]

\[\Rightarrow PA + PB \]

\[\Rightarrow PA + PB\]

\[OR PA + PA\]

\[OR 2PA\]

\[= 2(10)\]

\[ Perimeter \;of\; ΔPCD \; is \; 20 \; cm,\; where \;CE = CA, \;DE = DB,\; PA = PB \]

Note: Tangents from the internal point to a circle are equal