Who's good at math I really need help?‼️‼️‼️‼️
1 answer:
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Answer:
Step-by-step explanation:
step 1
Find the value of x
we know that
----> by alternate interior angles
solve for x
Group terms
step 2
Find the measure of angle a
we know that
----> by vertical angles
substitute the value of x
step 3
Find the measure of angle b
we know that
----> by supplementary angles (form a linear pair)
we have
substitute
step 4
Find the measure of angle c
we know that
----> by vertical angles
we have
therefore
step 5
Find the measure of angle d
we know that
----> by corresponding angles
we have
therefore
step 6
Find the measure of angle e
we know that
----> by alternate exterior angles
we have
therefore
step 7
Find the measure of angle f
we know that
----> by vertical angles
we have
therefore
Answer:
3a) The value of x = 56
3b) The measure of ∠ H T M = 90°
3c) The radius of the circle = 53
Step-by-step explanation:
3a) ∵ A F is a tangent to the circle O at point F
∵ Secant AH intersects circle O at point T
∴ (A F)² = (A T)(A H)
∴ 7( x + 7) = (21)² ⇒ ÷ 7
∴ x + 7 = 63
∴ x = 63 - 7 = 56
3b) ∵ HM is a diameter
∴ The measure of the arc HM = 180° ⇒ semi-circle
∵ ∠ H T M is inscribed angle subtended by the arc HM
∴ m ∠ H T M = half the measure of arc HM
∴ m ∠ H T M = 180° ÷ 2 = 90°
3c) ∵ Δ H T M is a right angle triangle at T
∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem
∴ (H M)² = (90)² + (56)²
∴ (H M)² = 11236
∴ HM = = 106
∴ OM = 106 ÷ 2 = 53
∵ OM is the radius of the circle O
∴ The radius = 53