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)

$$Perimeterof\Delta PCD=PC+CD+PD$$

$$\Rightarrow PC+CE+ED+PD$$

$$\Rightarrow PC+CA+DB+PD$$

$$\Rightarrow PA+PB$$

$$\Rightarrow PA+PB$$

$$ORPA+PA$$

$$OR2PA$$

$$=2(10)$$

$$Perimeterof\Delta PCDis20cm,whereCE=CA,DE=DB,PA=PB$$

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