In the given figure, AB is diameter and PC is tangent to the circle with center O. If AP = 40 cm, CP = 20 cm, find the radius of the circle.

Let radius of circle be r cm. From figure, ⇒ AP = AB + BP ⇒ 40 = AO + OB + BP ⇒ 40 = r + r + BP ⇒ 40 = 2r + BP ⇒ BP = (40 - 2r) cm. We know that, Tangent at point of intersection and radius of circle are perpendicular to each other. In △OCP, ⇒ OP 2 = OC 2 + PC 2 ⇒ (OB + BP) 2 = OC 2 + PC 2 ⇒ (r + 40 - 2r) 2 = r 2 + 20 2 ⇒ (40 - r) 2 = r 2 + 400 ⇒ 1600 + r 2 - 80r = r 2 + 400 ⇒ r 2 - r 2 + 80r = 1600 - 400 ⇒ 80r = 1200 ⇒ r = = 15 cm. Hence, radius of circle = 15 cm.

Using remainder theorem, factorise 6x³ - 11x² - 3x + 2 completely.

View Answer Bookmark Now

In rhombus ABCD, the co-ordinates of point A and C are (2, -6) and (-4, 8) respectively. Find the equation of the diagonal BD.

View Answer Bookmark Now

The following table shows the distribution of the marks obtained by 50 students in an aptitude test.
Marks obtained No. of students
15 6
18 18
21 12
24 8
27 4
30 2
Find the mean, the median and the mode of the distribution.

Marks obtained	No. of students
15	6
18	18
21	12
24	8
27	4
30	2

View Answer Bookmark Now

Mathematics

In the given figure, AB is diameter and PC is tangent to the circle with center O. If AP = 40 cm, CP = 20 cm, find the radius of the circle.

Circles

Related Questions

Using remainder theorem, factorise 6x³ - 11x² - 3x + 2 completely.

In rhombus ABCD, the co-ordinates of point A and C are (2, -6) and (-4, 8) respectively. Find the equation of the diagonal BD.

The following table shows the distribution of the marks obtained by 50 students in an aptitude test.
Marks obtained No. of students
15 6
18 18
21 12
24 8
27 4
30 2
Find the mean, the median and the mode of the distribution.

Mathematics

In the given figure, AB is diameter and PC is tangent to the circle with center O. If AP = 40 cm, CP = 20 cm, find the radius of the circle.

Circles

Related Questions

Using remainder theorem, factorise 6x3 - 11x2 - 3x + 2 completely.

In rhombus ABCD, the co-ordinates of point A and C are (2, -6) and (-4, 8) respectively. Find the equation of the diagonal BD.

The following table shows the distribution of the marks obtained by 50 students in an aptitude test.Marks obtainedNo. of students15618182112248274302Find the mean, the median and the mode of the distribution.

Using remainder theorem, factorise 6x³ - 11x² - 3x + 2 completely.

The following table shows the distribution of the marks obtained by 50 students in an aptitude test.
Marks obtained No. of students
15 6
18 18
21 12
24 8
27 4
30 2
Find the mean, the median and the mode of the distribution.