#
A point p is outside at a distance of 13 cm from its center . a secant from p cuts the circle in Q and R such that QR =7cm and the segment PQ of the secant exterior to the circle is 9cm therefore the radius of circle

1
Log in to add a comment

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Let the center be O

draw perpendicular to the secant, cuts at E

now in ΔOEP

OP = 13 cm

EP = 3.5 + 9 = 12.5 cm

so, by Pythagoras theorem,

OE² = OP² - EP²

=(13)² - (12.5)² = 169 - 156.25

=12.75

now in ΔORE

by Pythagoras theorem,

radius , OR² = OE² +ER²

= 12.75 + 12.25 = 25

∴OR² =25

**radius , OR = 5 cm**

draw perpendicular to the secant, cuts at E

now in ΔOEP

OP = 13 cm

EP = 3.5 + 9 = 12.5 cm

so, by Pythagoras theorem,

OE² = OP² - EP²

=(13)² - (12.5)² = 169 - 156.25

=12.75

now in ΔORE

by Pythagoras theorem,

radius , OR² = OE² +ER²

= 12.75 + 12.25 = 25

∴OR² =25