Question

Right triangle. Find the exact values of x and y.​

Answer 1

x =
`√(51)` , y = 7

Explanation:

since PA is a tangent, then angle between tangent and radius at point of contact A is 90°

the triangle with radius x is right.

using Pythagoras' identity in the right triangle

x² + 7² = 10²

x² + 49 = 100 ( subtract 49 from both sides )

x² = 51 ( take square root of both sides )

x =
`√(51)`

since PB is a tangent then ∠ B = 90° and triangle with y is right

note that the segment from B to the centre is the radius and is equal to x

using Pythagoras' identity in this right triangle

y² + x² = 10²

y² + (
`√(51)` )² = 100

y² + 51 = 100 ( subtract 51 from both sides )

y² = 49 ( take square root of both sides )

y =
`√(49)` = 7

then x =
`√(51)` and x = 7